x^100=1 (уравнение)

Найду корень уравнения: x^100=1

Вы ввели

 100    
x    = 1

$$x^{100} = 1$$

Подробное решение

Дано уравнение
$$x^{100} = 1$$
Т.к. степень в ур-нии равна = 100 - содержит чётное число 100 в числителе, то
ур-ние будет иметь два действительных корня.
Извлечём корень 100-й степени из обеих частей ур-ния:
Получим:
$$\sqrt[100]{\left(1 x + 0\right)^{100}} = \sqrt[100]{1}$$
$$\sqrt[100]{\left(1 x + 0\right)^{100}} = \sqrt[100]{1} \left(-1\right)$$
или
$$x = 1$$
$$x = -1$$
Получим ответ: x = 1
Получим ответ: x = -1
или
$$x_{1} = -1$$
$$x_{2} = 1$$

Остальные 98 корня(ей) являются комплексными.
сделаем замену:
$$z = x$$
тогда ур-ние будет таким:
$$z^{100} = 1$$
Любое комплексное число можно представить так:
$$z = r e^{i p}$$
подставляем в уравнение
$$r^{100} e^{100 i p} = 1$$
где
$$r = 1$$
- модуль комплексного числа
Подставляем r:
$$e^{100 i p} = 1$$
Используя формулу Эйлера, найдём корни для p
$$i \sin{\left(100 p \right)} + \cos{\left(100 p \right)} = 1$$
значит
$$\cos{\left(100 p \right)} = 1$$
и
$$\sin{\left(100 p \right)} = 0$$
тогда
$$p = \frac{\pi N}{50}$$
где N=0,1,2,3,...
Перебирая значения N и подставив p в формулу для z
Значит, решением будет для z:
$$z_{1} = -1$$
$$z_{2} = 1$$
$$z_{3} = - i$$
$$z_{4} = i$$
$$z_{5} = - \cos{\left(\frac{\pi}{50} \right)} - i \sin{\left(\frac{\pi}{50} \right)}$$
$$z_{6} = - \cos{\left(\frac{\pi}{50} \right)} + i \sin{\left(\frac{\pi}{50} \right)}$$
$$z_{7} = \cos{\left(\frac{\pi}{50} \right)} - i \sin{\left(\frac{\pi}{50} \right)}$$
$$z_{8} = \cos{\left(\frac{\pi}{50} \right)} + i \sin{\left(\frac{\pi}{50} \right)}$$
$$z_{9} = - \cos{\left(\frac{\pi}{25} \right)} - i \sin{\left(\frac{\pi}{25} \right)}$$
$$z_{10} = - \cos{\left(\frac{\pi}{25} \right)} + i \sin{\left(\frac{\pi}{25} \right)}$$
$$z_{11} = \cos{\left(\frac{\pi}{25} \right)} - i \sin{\left(\frac{\pi}{25} \right)}$$
$$z_{12} = \cos{\left(\frac{\pi}{25} \right)} + i \sin{\left(\frac{\pi}{25} \right)}$$
$$z_{13} = - \cos{\left(\frac{3 \pi}{50} \right)} - i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$z_{14} = - \cos{\left(\frac{3 \pi}{50} \right)} + i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$z_{15} = \cos{\left(\frac{3 \pi}{50} \right)} - i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$z_{16} = \cos{\left(\frac{3 \pi}{50} \right)} + i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$z_{17} = - \cos{\left(\frac{2 \pi}{25} \right)} - i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$z_{18} = - \cos{\left(\frac{2 \pi}{25} \right)} + i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$z_{19} = \cos{\left(\frac{2 \pi}{25} \right)} - i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$z_{20} = \cos{\left(\frac{2 \pi}{25} \right)} + i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$z_{21} = - \cos{\left(\frac{3 \pi}{25} \right)} - i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$z_{22} = - \cos{\left(\frac{3 \pi}{25} \right)} + i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$z_{23} = \cos{\left(\frac{3 \pi}{25} \right)} - i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$z_{24} = \cos{\left(\frac{3 \pi}{25} \right)} + i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$z_{25} = - \cos{\left(\frac{7 \pi}{50} \right)} - i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$z_{26} = - \cos{\left(\frac{7 \pi}{50} \right)} + i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$z_{27} = \cos{\left(\frac{7 \pi}{50} \right)} - i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$z_{28} = \cos{\left(\frac{7 \pi}{50} \right)} + i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$z_{29} = - \cos{\left(\frac{4 \pi}{25} \right)} - i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$z_{30} = - \cos{\left(\frac{4 \pi}{25} \right)} + i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$z_{31} = \cos{\left(\frac{4 \pi}{25} \right)} - i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$z_{32} = \cos{\left(\frac{4 \pi}{25} \right)} + i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$z_{33} = - \cos{\left(\frac{9 \pi}{50} \right)} - i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$z_{34} = - \cos{\left(\frac{9 \pi}{50} \right)} + i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$z_{35} = \cos{\left(\frac{9 \pi}{50} \right)} - i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$z_{36} = \cos{\left(\frac{9 \pi}{50} \right)} + i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$z_{37} = - \cos{\left(\frac{11 \pi}{50} \right)} - i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$z_{38} = - \cos{\left(\frac{11 \pi}{50} \right)} + i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$z_{39} = \cos{\left(\frac{11 \pi}{50} \right)} - i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$z_{40} = \cos{\left(\frac{11 \pi}{50} \right)} + i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$z_{41} = - \cos{\left(\frac{6 \pi}{25} \right)} - i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$z_{42} = - \cos{\left(\frac{6 \pi}{25} \right)} + i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$z_{43} = \cos{\left(\frac{6 \pi}{25} \right)} - i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$z_{44} = \cos{\left(\frac{6 \pi}{25} \right)} + i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$z_{45} = - \cos{\left(\frac{13 \pi}{50} \right)} - i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$z_{46} = - \cos{\left(\frac{13 \pi}{50} \right)} + i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$z_{47} = \cos{\left(\frac{13 \pi}{50} \right)} - i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$z_{48} = \cos{\left(\frac{13 \pi}{50} \right)} + i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$z_{49} = - \cos{\left(\frac{7 \pi}{25} \right)} - i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$z_{50} = - \cos{\left(\frac{7 \pi}{25} \right)} + i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$z_{51} = \cos{\left(\frac{7 \pi}{25} \right)} - i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$z_{52} = \cos{\left(\frac{7 \pi}{25} \right)} + i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$z_{53} = - \cos{\left(\frac{8 \pi}{25} \right)} - i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$z_{54} = - \cos{\left(\frac{8 \pi}{25} \right)} + i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$z_{55} = \cos{\left(\frac{8 \pi}{25} \right)} - i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$z_{56} = \cos{\left(\frac{8 \pi}{25} \right)} + i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$z_{57} = - \cos{\left(\frac{17 \pi}{50} \right)} - i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$z_{58} = - \cos{\left(\frac{17 \pi}{50} \right)} + i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$z_{59} = \cos{\left(\frac{17 \pi}{50} \right)} - i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$z_{60} = \cos{\left(\frac{17 \pi}{50} \right)} + i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$z_{61} = - \cos{\left(\frac{9 \pi}{25} \right)} - i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$z_{62} = - \cos{\left(\frac{9 \pi}{25} \right)} + i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$z_{63} = \cos{\left(\frac{9 \pi}{25} \right)} - i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$z_{64} = \cos{\left(\frac{9 \pi}{25} \right)} + i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$z_{65} = - \cos{\left(\frac{19 \pi}{50} \right)} - i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$z_{66} = - \cos{\left(\frac{19 \pi}{50} \right)} + i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$z_{67} = \cos{\left(\frac{19 \pi}{50} \right)} - i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$z_{68} = \cos{\left(\frac{19 \pi}{50} \right)} + i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$z_{69} = - \cos{\left(\frac{21 \pi}{50} \right)} - i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$z_{70} = - \cos{\left(\frac{21 \pi}{50} \right)} + i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$z_{71} = \cos{\left(\frac{21 \pi}{50} \right)} - i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$z_{72} = \cos{\left(\frac{21 \pi}{50} \right)} + i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$z_{73} = - \cos{\left(\frac{11 \pi}{25} \right)} - i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$z_{74} = - \cos{\left(\frac{11 \pi}{25} \right)} + i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$z_{75} = \cos{\left(\frac{11 \pi}{25} \right)} - i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$z_{76} = \cos{\left(\frac{11 \pi}{25} \right)} + i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$z_{77} = - \cos{\left(\frac{23 \pi}{50} \right)} - i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$z_{78} = - \cos{\left(\frac{23 \pi}{50} \right)} + i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$z_{79} = \cos{\left(\frac{23 \pi}{50} \right)} - i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$z_{80} = \cos{\left(\frac{23 \pi}{50} \right)} + i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$z_{81} = - \cos{\left(\frac{12 \pi}{25} \right)} - i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$z_{82} = - \cos{\left(\frac{12 \pi}{25} \right)} + i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$z_{83} = \cos{\left(\frac{12 \pi}{25} \right)} - i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$z_{84} = \cos{\left(\frac{12 \pi}{25} \right)} + i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$z_{85} = - \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$z_{86} = - \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$z_{87} = \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$z_{88} = \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$z_{89} = - \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$z_{90} = - \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$z_{91} = - \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$z_{92} = - \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$z_{93} = - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$z_{94} = - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \frac{\sqrt{5} i}{4} - \frac{i}{4}$$
$$z_{95} = \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$z_{96} = \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \frac{\sqrt{5} i}{4} - \frac{i}{4}$$
$$z_{97} = - \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$z_{98} = - \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt{5} i}{4} + \frac{i}{4}$$
$$z_{99} = \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$z_{100} = \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt{5} i}{4} + \frac{i}{4}$$
делаем обратную замену
$$z = x$$
$$x = z$$

Тогда, окончательный ответ:
$$x_{1} = -1$$
$$x_{2} = 1$$
$$x_{3} = - i$$
$$x_{4} = i$$
$$x_{5} = - \cos{\left(\frac{\pi}{50} \right)} - i \sin{\left(\frac{\pi}{50} \right)}$$
$$x_{6} = - \cos{\left(\frac{\pi}{50} \right)} + i \sin{\left(\frac{\pi}{50} \right)}$$
$$x_{7} = \cos{\left(\frac{\pi}{50} \right)} - i \sin{\left(\frac{\pi}{50} \right)}$$
$$x_{8} = \cos{\left(\frac{\pi}{50} \right)} + i \sin{\left(\frac{\pi}{50} \right)}$$
$$x_{9} = - \cos{\left(\frac{\pi}{25} \right)} - i \sin{\left(\frac{\pi}{25} \right)}$$
$$x_{10} = - \cos{\left(\frac{\pi}{25} \right)} + i \sin{\left(\frac{\pi}{25} \right)}$$
$$x_{11} = \cos{\left(\frac{\pi}{25} \right)} - i \sin{\left(\frac{\pi}{25} \right)}$$
$$x_{12} = \cos{\left(\frac{\pi}{25} \right)} + i \sin{\left(\frac{\pi}{25} \right)}$$
$$x_{13} = - \cos{\left(\frac{3 \pi}{50} \right)} - i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$x_{14} = - \cos{\left(\frac{3 \pi}{50} \right)} + i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$x_{15} = \cos{\left(\frac{3 \pi}{50} \right)} - i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$x_{16} = \cos{\left(\frac{3 \pi}{50} \right)} + i \sin{\left(\frac{3 \pi}{50} \right)}$$
$$x_{17} = - \cos{\left(\frac{2 \pi}{25} \right)} - i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$x_{18} = - \cos{\left(\frac{2 \pi}{25} \right)} + i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$x_{19} = \cos{\left(\frac{2 \pi}{25} \right)} - i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$x_{20} = \cos{\left(\frac{2 \pi}{25} \right)} + i \sin{\left(\frac{2 \pi}{25} \right)}$$
$$x_{21} = - \cos{\left(\frac{3 \pi}{25} \right)} - i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$x_{22} = - \cos{\left(\frac{3 \pi}{25} \right)} + i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$x_{23} = \cos{\left(\frac{3 \pi}{25} \right)} - i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$x_{24} = \cos{\left(\frac{3 \pi}{25} \right)} + i \sin{\left(\frac{3 \pi}{25} \right)}$$
$$x_{25} = - \cos{\left(\frac{7 \pi}{50} \right)} - i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$x_{26} = - \cos{\left(\frac{7 \pi}{50} \right)} + i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$x_{27} = \cos{\left(\frac{7 \pi}{50} \right)} - i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$x_{28} = \cos{\left(\frac{7 \pi}{50} \right)} + i \sin{\left(\frac{7 \pi}{50} \right)}$$
$$x_{29} = - \cos{\left(\frac{4 \pi}{25} \right)} - i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$x_{30} = - \cos{\left(\frac{4 \pi}{25} \right)} + i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$x_{31} = \cos{\left(\frac{4 \pi}{25} \right)} - i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$x_{32} = \cos{\left(\frac{4 \pi}{25} \right)} + i \sin{\left(\frac{4 \pi}{25} \right)}$$
$$x_{33} = - \cos{\left(\frac{9 \pi}{50} \right)} - i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$x_{34} = - \cos{\left(\frac{9 \pi}{50} \right)} + i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$x_{35} = \cos{\left(\frac{9 \pi}{50} \right)} - i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$x_{36} = \cos{\left(\frac{9 \pi}{50} \right)} + i \sin{\left(\frac{9 \pi}{50} \right)}$$
$$x_{37} = - \cos{\left(\frac{11 \pi}{50} \right)} - i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$x_{38} = - \cos{\left(\frac{11 \pi}{50} \right)} + i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$x_{39} = \cos{\left(\frac{11 \pi}{50} \right)} - i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$x_{40} = \cos{\left(\frac{11 \pi}{50} \right)} + i \sin{\left(\frac{11 \pi}{50} \right)}$$
$$x_{41} = - \cos{\left(\frac{6 \pi}{25} \right)} - i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$x_{42} = - \cos{\left(\frac{6 \pi}{25} \right)} + i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$x_{43} = \cos{\left(\frac{6 \pi}{25} \right)} - i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$x_{44} = \cos{\left(\frac{6 \pi}{25} \right)} + i \sin{\left(\frac{6 \pi}{25} \right)}$$
$$x_{45} = - \cos{\left(\frac{13 \pi}{50} \right)} - i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$x_{46} = - \cos{\left(\frac{13 \pi}{50} \right)} + i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$x_{47} = \cos{\left(\frac{13 \pi}{50} \right)} - i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$x_{48} = \cos{\left(\frac{13 \pi}{50} \right)} + i \sin{\left(\frac{13 \pi}{50} \right)}$$
$$x_{49} = - \cos{\left(\frac{7 \pi}{25} \right)} - i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$x_{50} = - \cos{\left(\frac{7 \pi}{25} \right)} + i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$x_{51} = \cos{\left(\frac{7 \pi}{25} \right)} - i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$x_{52} = \cos{\left(\frac{7 \pi}{25} \right)} + i \sin{\left(\frac{7 \pi}{25} \right)}$$
$$x_{53} = - \cos{\left(\frac{8 \pi}{25} \right)} - i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$x_{54} = - \cos{\left(\frac{8 \pi}{25} \right)} + i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$x_{55} = \cos{\left(\frac{8 \pi}{25} \right)} - i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$x_{56} = \cos{\left(\frac{8 \pi}{25} \right)} + i \sin{\left(\frac{8 \pi}{25} \right)}$$
$$x_{57} = - \cos{\left(\frac{17 \pi}{50} \right)} - i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$x_{58} = - \cos{\left(\frac{17 \pi}{50} \right)} + i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$x_{59} = \cos{\left(\frac{17 \pi}{50} \right)} - i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$x_{60} = \cos{\left(\frac{17 \pi}{50} \right)} + i \sin{\left(\frac{17 \pi}{50} \right)}$$
$$x_{61} = - \cos{\left(\frac{9 \pi}{25} \right)} - i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$x_{62} = - \cos{\left(\frac{9 \pi}{25} \right)} + i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$x_{63} = \cos{\left(\frac{9 \pi}{25} \right)} - i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$x_{64} = \cos{\left(\frac{9 \pi}{25} \right)} + i \sin{\left(\frac{9 \pi}{25} \right)}$$
$$x_{65} = - \cos{\left(\frac{19 \pi}{50} \right)} - i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$x_{66} = - \cos{\left(\frac{19 \pi}{50} \right)} + i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$x_{67} = \cos{\left(\frac{19 \pi}{50} \right)} - i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$x_{68} = \cos{\left(\frac{19 \pi}{50} \right)} + i \sin{\left(\frac{19 \pi}{50} \right)}$$
$$x_{69} = - \cos{\left(\frac{21 \pi}{50} \right)} - i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$x_{70} = - \cos{\left(\frac{21 \pi}{50} \right)} + i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$x_{71} = \cos{\left(\frac{21 \pi}{50} \right)} - i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$x_{72} = \cos{\left(\frac{21 \pi}{50} \right)} + i \sin{\left(\frac{21 \pi}{50} \right)}$$
$$x_{73} = - \cos{\left(\frac{11 \pi}{25} \right)} - i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$x_{74} = - \cos{\left(\frac{11 \pi}{25} \right)} + i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$x_{75} = \cos{\left(\frac{11 \pi}{25} \right)} - i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$x_{76} = \cos{\left(\frac{11 \pi}{25} \right)} + i \sin{\left(\frac{11 \pi}{25} \right)}$$
$$x_{77} = - \cos{\left(\frac{23 \pi}{50} \right)} - i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$x_{78} = - \cos{\left(\frac{23 \pi}{50} \right)} + i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$x_{79} = \cos{\left(\frac{23 \pi}{50} \right)} - i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$x_{80} = \cos{\left(\frac{23 \pi}{50} \right)} + i \sin{\left(\frac{23 \pi}{50} \right)}$$
$$x_{81} = - \cos{\left(\frac{12 \pi}{25} \right)} - i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$x_{82} = - \cos{\left(\frac{12 \pi}{25} \right)} + i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$x_{83} = \cos{\left(\frac{12 \pi}{25} \right)} - i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$x_{84} = \cos{\left(\frac{12 \pi}{25} \right)} + i \sin{\left(\frac{12 \pi}{25} \right)}$$
$$x_{85} = - \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$x_{86} = - \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$x_{87} = \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$x_{88} = \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$x_{89} = - \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$x_{90} = - \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$
$$x_{91} = - \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$x_{92} = - \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$
$$x_{93} = - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$x_{94} = - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \frac{\sqrt{5} i}{4} - \frac{i}{4}$$
$$x_{95} = \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$x_{96} = \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \frac{\sqrt{5} i}{4} - \frac{i}{4}$$
$$x_{97} = - \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$x_{98} = - \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt{5} i}{4} + \frac{i}{4}$$
$$x_{99} = \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{i}{4} + \frac{\sqrt{5} i}{4}$$
$$x_{100} = \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt{5} i}{4} + \frac{i}{4}$$

Быстрый ответ

x1 = -1

$$x_{1} = -1$$

x2 = 1

$$x_{2} = 1$$

            ___________                
           /       ___      /      ___\
          /  5   \/ 5       |1   \/ 5 |
x3 = -   /   - - -----  + I*|- + -----|
       \/    8     8        \4     4  /

$$x_{3} = - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + i \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)$$

            ___________                  
           /       ___      /        ___\
          /  5   \/ 5       |  1   \/ 5 |
x4 = -   /   - - -----  + I*|- - - -----|
       \/    8     8        \  4     4  /

$$x_{4} = - \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + i \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)$$

          ___________                
         /       ___      /      ___\
        /  5   \/ 5       |1   \/ 5 |
x5 =   /   - - -----  + I*|- + -----|
     \/    8     8        \4     4  /

$$x_{5} = \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + i \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)$$

          ___________                  
         /       ___      /        ___\
        /  5   \/ 5       |  1   \/ 5 |
x6 =   /   - - -----  + I*|- - - -----|
     \/    8     8        \  4     4  /

$$x_{6} = \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + i \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)$$

            ___________                  
           /       ___      /        ___\
          /  5   \/ 5       |  1   \/ 5 |
x7 = -   /   - + -----  + I*|- - + -----|
       \/    8     8        \  4     4  /

$$x_{7} = - \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + i \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right)$$

            ___________                
           /       ___      /      ___\
          /  5   \/ 5       |1   \/ 5 |
x8 = -   /   - + -----  + I*|- - -----|
       \/    8     8        \4     4  /

$$x_{8} = - \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + i \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)$$

          ___________                  
         /       ___      /        ___\
        /  5   \/ 5       |  1   \/ 5 |
x9 =   /   - + -----  + I*|- - + -----|
     \/    8     8        \  4     4  /

$$x_{9} = \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + i \left(- \frac{1}{4} + \frac{\sqrt{5}}{4}\right)$$

           ___________                
          /       ___      /      ___\
         /  5   \/ 5       |1   \/ 5 |
x10 =   /   - + -----  + I*|- - -----|
      \/    8     8        \4     4  /

$$x_{10} = \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} + i \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right)$$

x11 = -I

$$x_{11} = - i$$

x12 = I

$$x_{12} = i$$

           /pi\        /pi\
x13 = - cos|--| - I*sin|--|
           \50/        \50/

$$x_{13} = - \cos{\left(\frac{\pi}{50} \right)} - i \sin{\left(\frac{\pi}{50} \right)}$$

           /pi\        /pi\
x14 = - cos|--| + I*sin|--|
           \50/        \50/

$$x_{14} = - \cos{\left(\frac{\pi}{50} \right)} + i \sin{\left(\frac{\pi}{50} \right)}$$

             /pi\      /pi\
x15 = - I*sin|--| + cos|--|
             \50/      \50/

$$x_{15} = \cos{\left(\frac{\pi}{50} \right)} - i \sin{\left(\frac{\pi}{50} \right)}$$

           /pi\      /pi\
x16 = I*sin|--| + cos|--|
           \50/      \50/

$$x_{16} = \cos{\left(\frac{\pi}{50} \right)} + i \sin{\left(\frac{\pi}{50} \right)}$$

           /pi\        /pi\
x17 = - cos|--| - I*sin|--|
           \25/        \25/

$$x_{17} = - \cos{\left(\frac{\pi}{25} \right)} - i \sin{\left(\frac{\pi}{25} \right)}$$

           /pi\        /pi\
x18 = - cos|--| + I*sin|--|
           \25/        \25/

$$x_{18} = - \cos{\left(\frac{\pi}{25} \right)} + i \sin{\left(\frac{\pi}{25} \right)}$$

             /pi\      /pi\
x19 = - I*sin|--| + cos|--|
             \25/      \25/

$$x_{19} = \cos{\left(\frac{\pi}{25} \right)} - i \sin{\left(\frac{\pi}{25} \right)}$$

           /pi\      /pi\
x20 = I*sin|--| + cos|--|
           \25/      \25/

$$x_{20} = \cos{\left(\frac{\pi}{25} \right)} + i \sin{\left(\frac{\pi}{25} \right)}$$

           /3*pi\        /3*pi\
x21 = - cos|----| - I*sin|----|
           \ 50 /        \ 50 /

$$x_{21} = - \cos{\left(\frac{3 \pi}{50} \right)} - i \sin{\left(\frac{3 \pi}{50} \right)}$$

           /3*pi\        /3*pi\
x22 = - cos|----| + I*sin|----|
           \ 50 /        \ 50 /

$$x_{22} = - \cos{\left(\frac{3 \pi}{50} \right)} + i \sin{\left(\frac{3 \pi}{50} \right)}$$

             /3*pi\      /3*pi\
x23 = - I*sin|----| + cos|----|
             \ 50 /      \ 50 /

$$x_{23} = \cos{\left(\frac{3 \pi}{50} \right)} - i \sin{\left(\frac{3 \pi}{50} \right)}$$

           /3*pi\      /3*pi\
x24 = I*sin|----| + cos|----|
           \ 50 /      \ 50 /

$$x_{24} = \cos{\left(\frac{3 \pi}{50} \right)} + i \sin{\left(\frac{3 \pi}{50} \right)}$$

           /2*pi\        /2*pi\
x25 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{25} = - \cos{\left(\frac{2 \pi}{25} \right)} - i \sin{\left(\frac{2 \pi}{25} \right)}$$

           /2*pi\        /2*pi\
x26 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{26} = - \cos{\left(\frac{2 \pi}{25} \right)} + i \sin{\left(\frac{2 \pi}{25} \right)}$$

             /2*pi\      /2*pi\
x27 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{27} = \cos{\left(\frac{2 \pi}{25} \right)} - i \sin{\left(\frac{2 \pi}{25} \right)}$$

           /2*pi\      /2*pi\
x28 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{28} = \cos{\left(\frac{2 \pi}{25} \right)} + i \sin{\left(\frac{2 \pi}{25} \right)}$$

           /3*pi\        /3*pi\
x29 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{29} = - \cos{\left(\frac{3 \pi}{25} \right)} - i \sin{\left(\frac{3 \pi}{25} \right)}$$

           /3*pi\        /3*pi\
x30 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{30} = - \cos{\left(\frac{3 \pi}{25} \right)} + i \sin{\left(\frac{3 \pi}{25} \right)}$$

             /3*pi\      /3*pi\
x31 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{31} = \cos{\left(\frac{3 \pi}{25} \right)} - i \sin{\left(\frac{3 \pi}{25} \right)}$$

           /3*pi\      /3*pi\
x32 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{32} = \cos{\left(\frac{3 \pi}{25} \right)} + i \sin{\left(\frac{3 \pi}{25} \right)}$$

           /7*pi\        /7*pi\
x33 = - cos|----| - I*sin|----|
           \ 50 /        \ 50 /

$$x_{33} = - \cos{\left(\frac{7 \pi}{50} \right)} - i \sin{\left(\frac{7 \pi}{50} \right)}$$

           /7*pi\        /7*pi\
x34 = - cos|----| + I*sin|----|
           \ 50 /        \ 50 /

$$x_{34} = - \cos{\left(\frac{7 \pi}{50} \right)} + i \sin{\left(\frac{7 \pi}{50} \right)}$$

             /7*pi\      /7*pi\
x35 = - I*sin|----| + cos|----|
             \ 50 /      \ 50 /

$$x_{35} = \cos{\left(\frac{7 \pi}{50} \right)} - i \sin{\left(\frac{7 \pi}{50} \right)}$$

           /7*pi\      /7*pi\
x36 = I*sin|----| + cos|----|
           \ 50 /      \ 50 /

$$x_{36} = \cos{\left(\frac{7 \pi}{50} \right)} + i \sin{\left(\frac{7 \pi}{50} \right)}$$

           /4*pi\        /4*pi\
x37 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{37} = - \cos{\left(\frac{4 \pi}{25} \right)} - i \sin{\left(\frac{4 \pi}{25} \right)}$$

           /4*pi\        /4*pi\
x38 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{38} = - \cos{\left(\frac{4 \pi}{25} \right)} + i \sin{\left(\frac{4 \pi}{25} \right)}$$

             /4*pi\      /4*pi\
x39 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{39} = \cos{\left(\frac{4 \pi}{25} \right)} - i \sin{\left(\frac{4 \pi}{25} \right)}$$

           /4*pi\      /4*pi\
x40 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{40} = \cos{\left(\frac{4 \pi}{25} \right)} + i \sin{\left(\frac{4 \pi}{25} \right)}$$

           /9*pi\        /9*pi\
x41 = - cos|----| - I*sin|----|
           \ 50 /        \ 50 /

$$x_{41} = - \cos{\left(\frac{9 \pi}{50} \right)} - i \sin{\left(\frac{9 \pi}{50} \right)}$$

           /9*pi\        /9*pi\
x42 = - cos|----| + I*sin|----|
           \ 50 /        \ 50 /

$$x_{42} = - \cos{\left(\frac{9 \pi}{50} \right)} + i \sin{\left(\frac{9 \pi}{50} \right)}$$

             /9*pi\      /9*pi\
x43 = - I*sin|----| + cos|----|
             \ 50 /      \ 50 /

$$x_{43} = \cos{\left(\frac{9 \pi}{50} \right)} - i \sin{\left(\frac{9 \pi}{50} \right)}$$

           /9*pi\      /9*pi\
x44 = I*sin|----| + cos|----|
           \ 50 /      \ 50 /

$$x_{44} = \cos{\left(\frac{9 \pi}{50} \right)} + i \sin{\left(\frac{9 \pi}{50} \right)}$$

           /11*pi\        /11*pi\
x45 = - cos|-----| - I*sin|-----|
           \  50 /        \  50 /

$$x_{45} = - \cos{\left(\frac{11 \pi}{50} \right)} - i \sin{\left(\frac{11 \pi}{50} \right)}$$

           /11*pi\        /11*pi\
x46 = - cos|-----| + I*sin|-----|
           \  50 /        \  50 /

$$x_{46} = - \cos{\left(\frac{11 \pi}{50} \right)} + i \sin{\left(\frac{11 \pi}{50} \right)}$$

             /11*pi\      /11*pi\
x47 = - I*sin|-----| + cos|-----|
             \  50 /      \  50 /

$$x_{47} = \cos{\left(\frac{11 \pi}{50} \right)} - i \sin{\left(\frac{11 \pi}{50} \right)}$$

           /11*pi\      /11*pi\
x48 = I*sin|-----| + cos|-----|
           \  50 /      \  50 /

$$x_{48} = \cos{\left(\frac{11 \pi}{50} \right)} + i \sin{\left(\frac{11 \pi}{50} \right)}$$

           /6*pi\        /6*pi\
x49 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{49} = - \cos{\left(\frac{6 \pi}{25} \right)} - i \sin{\left(\frac{6 \pi}{25} \right)}$$

           /6*pi\        /6*pi\
x50 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{50} = - \cos{\left(\frac{6 \pi}{25} \right)} + i \sin{\left(\frac{6 \pi}{25} \right)}$$

             /6*pi\      /6*pi\
x51 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{51} = \cos{\left(\frac{6 \pi}{25} \right)} - i \sin{\left(\frac{6 \pi}{25} \right)}$$

           /6*pi\      /6*pi\
x52 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{52} = \cos{\left(\frac{6 \pi}{25} \right)} + i \sin{\left(\frac{6 \pi}{25} \right)}$$

           /13*pi\        /13*pi\
x53 = - cos|-----| - I*sin|-----|
           \  50 /        \  50 /

$$x_{53} = - \cos{\left(\frac{13 \pi}{50} \right)} - i \sin{\left(\frac{13 \pi}{50} \right)}$$

           /13*pi\        /13*pi\
x54 = - cos|-----| + I*sin|-----|
           \  50 /        \  50 /

$$x_{54} = - \cos{\left(\frac{13 \pi}{50} \right)} + i \sin{\left(\frac{13 \pi}{50} \right)}$$

             /13*pi\      /13*pi\
x55 = - I*sin|-----| + cos|-----|
             \  50 /      \  50 /

$$x_{55} = \cos{\left(\frac{13 \pi}{50} \right)} - i \sin{\left(\frac{13 \pi}{50} \right)}$$

           /13*pi\      /13*pi\
x56 = I*sin|-----| + cos|-----|
           \  50 /      \  50 /

$$x_{56} = \cos{\left(\frac{13 \pi}{50} \right)} + i \sin{\left(\frac{13 \pi}{50} \right)}$$

           /7*pi\        /7*pi\
x57 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{57} = - \cos{\left(\frac{7 \pi}{25} \right)} - i \sin{\left(\frac{7 \pi}{25} \right)}$$

           /7*pi\        /7*pi\
x58 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{58} = - \cos{\left(\frac{7 \pi}{25} \right)} + i \sin{\left(\frac{7 \pi}{25} \right)}$$

             /7*pi\      /7*pi\
x59 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{59} = \cos{\left(\frac{7 \pi}{25} \right)} - i \sin{\left(\frac{7 \pi}{25} \right)}$$

           /7*pi\      /7*pi\
x60 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{60} = \cos{\left(\frac{7 \pi}{25} \right)} + i \sin{\left(\frac{7 \pi}{25} \right)}$$

           /8*pi\        /8*pi\
x61 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{61} = - \cos{\left(\frac{8 \pi}{25} \right)} - i \sin{\left(\frac{8 \pi}{25} \right)}$$

           /8*pi\        /8*pi\
x62 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{62} = - \cos{\left(\frac{8 \pi}{25} \right)} + i \sin{\left(\frac{8 \pi}{25} \right)}$$

             /8*pi\      /8*pi\
x63 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{63} = \cos{\left(\frac{8 \pi}{25} \right)} - i \sin{\left(\frac{8 \pi}{25} \right)}$$

           /8*pi\      /8*pi\
x64 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{64} = \cos{\left(\frac{8 \pi}{25} \right)} + i \sin{\left(\frac{8 \pi}{25} \right)}$$

           /17*pi\        /17*pi\
x65 = - cos|-----| - I*sin|-----|
           \  50 /        \  50 /

$$x_{65} = - \cos{\left(\frac{17 \pi}{50} \right)} - i \sin{\left(\frac{17 \pi}{50} \right)}$$

           /17*pi\        /17*pi\
x66 = - cos|-----| + I*sin|-----|
           \  50 /        \  50 /

$$x_{66} = - \cos{\left(\frac{17 \pi}{50} \right)} + i \sin{\left(\frac{17 \pi}{50} \right)}$$

             /17*pi\      /17*pi\
x67 = - I*sin|-----| + cos|-----|
             \  50 /      \  50 /

$$x_{67} = \cos{\left(\frac{17 \pi}{50} \right)} - i \sin{\left(\frac{17 \pi}{50} \right)}$$

           /17*pi\      /17*pi\
x68 = I*sin|-----| + cos|-----|
           \  50 /      \  50 /

$$x_{68} = \cos{\left(\frac{17 \pi}{50} \right)} + i \sin{\left(\frac{17 \pi}{50} \right)}$$

           /9*pi\        /9*pi\
x69 = - cos|----| - I*sin|----|
           \ 25 /        \ 25 /

$$x_{69} = - \cos{\left(\frac{9 \pi}{25} \right)} - i \sin{\left(\frac{9 \pi}{25} \right)}$$

           /9*pi\        /9*pi\
x70 = - cos|----| + I*sin|----|
           \ 25 /        \ 25 /

$$x_{70} = - \cos{\left(\frac{9 \pi}{25} \right)} + i \sin{\left(\frac{9 \pi}{25} \right)}$$

             /9*pi\      /9*pi\
x71 = - I*sin|----| + cos|----|
             \ 25 /      \ 25 /

$$x_{71} = \cos{\left(\frac{9 \pi}{25} \right)} - i \sin{\left(\frac{9 \pi}{25} \right)}$$

           /9*pi\      /9*pi\
x72 = I*sin|----| + cos|----|
           \ 25 /      \ 25 /

$$x_{72} = \cos{\left(\frac{9 \pi}{25} \right)} + i \sin{\left(\frac{9 \pi}{25} \right)}$$

           /19*pi\        /19*pi\
x73 = - cos|-----| - I*sin|-----|
           \  50 /        \  50 /

$$x_{73} = - \cos{\left(\frac{19 \pi}{50} \right)} - i \sin{\left(\frac{19 \pi}{50} \right)}$$

           /19*pi\        /19*pi\
x74 = - cos|-----| + I*sin|-----|
           \  50 /        \  50 /

$$x_{74} = - \cos{\left(\frac{19 \pi}{50} \right)} + i \sin{\left(\frac{19 \pi}{50} \right)}$$

             /19*pi\      /19*pi\
x75 = - I*sin|-----| + cos|-----|
             \  50 /      \  50 /

$$x_{75} = \cos{\left(\frac{19 \pi}{50} \right)} - i \sin{\left(\frac{19 \pi}{50} \right)}$$

           /19*pi\      /19*pi\
x76 = I*sin|-----| + cos|-----|
           \  50 /      \  50 /

$$x_{76} = \cos{\left(\frac{19 \pi}{50} \right)} + i \sin{\left(\frac{19 \pi}{50} \right)}$$

           /21*pi\        /21*pi\
x77 = - cos|-----| - I*sin|-----|
           \  50 /        \  50 /

$$x_{77} = - \cos{\left(\frac{21 \pi}{50} \right)} - i \sin{\left(\frac{21 \pi}{50} \right)}$$

           /21*pi\        /21*pi\
x78 = - cos|-----| + I*sin|-----|
           \  50 /        \  50 /

$$x_{78} = - \cos{\left(\frac{21 \pi}{50} \right)} + i \sin{\left(\frac{21 \pi}{50} \right)}$$

             /21*pi\      /21*pi\
x79 = - I*sin|-----| + cos|-----|
             \  50 /      \  50 /

$$x_{79} = \cos{\left(\frac{21 \pi}{50} \right)} - i \sin{\left(\frac{21 \pi}{50} \right)}$$

           /21*pi\      /21*pi\
x80 = I*sin|-----| + cos|-----|
           \  50 /      \  50 /

$$x_{80} = \cos{\left(\frac{21 \pi}{50} \right)} + i \sin{\left(\frac{21 \pi}{50} \right)}$$

           /11*pi\        /11*pi\
x81 = - cos|-----| - I*sin|-----|
           \  25 /        \  25 /

$$x_{81} = - \cos{\left(\frac{11 \pi}{25} \right)} - i \sin{\left(\frac{11 \pi}{25} \right)}$$

           /11*pi\        /11*pi\
x82 = - cos|-----| + I*sin|-----|
           \  25 /        \  25 /

$$x_{82} = - \cos{\left(\frac{11 \pi}{25} \right)} + i \sin{\left(\frac{11 \pi}{25} \right)}$$

             /11*pi\      /11*pi\
x83 = - I*sin|-----| + cos|-----|
             \  25 /      \  25 /

$$x_{83} = \cos{\left(\frac{11 \pi}{25} \right)} - i \sin{\left(\frac{11 \pi}{25} \right)}$$

           /11*pi\      /11*pi\
x84 = I*sin|-----| + cos|-----|
           \  25 /      \  25 /

$$x_{84} = \cos{\left(\frac{11 \pi}{25} \right)} + i \sin{\left(\frac{11 \pi}{25} \right)}$$

           /23*pi\        /23*pi\
x85 = - cos|-----| - I*sin|-----|
           \  50 /        \  50 /

$$x_{85} = - \cos{\left(\frac{23 \pi}{50} \right)} - i \sin{\left(\frac{23 \pi}{50} \right)}$$

           /23*pi\        /23*pi\
x86 = - cos|-----| + I*sin|-----|
           \  50 /        \  50 /

$$x_{86} = - \cos{\left(\frac{23 \pi}{50} \right)} + i \sin{\left(\frac{23 \pi}{50} \right)}$$

             /23*pi\      /23*pi\
x87 = - I*sin|-----| + cos|-----|
             \  50 /      \  50 /

$$x_{87} = \cos{\left(\frac{23 \pi}{50} \right)} - i \sin{\left(\frac{23 \pi}{50} \right)}$$

           /23*pi\      /23*pi\
x88 = I*sin|-----| + cos|-----|
           \  50 /      \  50 /

$$x_{88} = \cos{\left(\frac{23 \pi}{50} \right)} + i \sin{\left(\frac{23 \pi}{50} \right)}$$

           /12*pi\        /12*pi\
x89 = - cos|-----| - I*sin|-----|
           \  25 /        \  25 /

$$x_{89} = - \cos{\left(\frac{12 \pi}{25} \right)} - i \sin{\left(\frac{12 \pi}{25} \right)}$$

           /12*pi\        /12*pi\
x90 = - cos|-----| + I*sin|-----|
           \  25 /        \  25 /

$$x_{90} = - \cos{\left(\frac{12 \pi}{25} \right)} + i \sin{\left(\frac{12 \pi}{25} \right)}$$

             /12*pi\      /12*pi\
x91 = - I*sin|-----| + cos|-----|
             \  25 /      \  25 /

$$x_{91} = \cos{\left(\frac{12 \pi}{25} \right)} - i \sin{\left(\frac{12 \pi}{25} \right)}$$

           /12*pi\      /12*pi\
x92 = I*sin|-----| + cos|-----|
           \  25 /      \  25 /

$$x_{92} = \cos{\left(\frac{12 \pi}{25} \right)} + i \sin{\left(\frac{12 \pi}{25} \right)}$$

                           ___________
              ___         /       ___ 
        1   \/ 5         /  5   \/ 5  
x93 = - - + ----- - I*  /   - + ----- 
        4     4       \/    8     8   

$$x_{93} = - \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$

                           ___________
              ___         /       ___ 
        1   \/ 5         /  5   \/ 5  
x94 = - - + ----- + I*  /   - + ----- 
        4     4       \/    8     8   

$$x_{94} = - \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$

                         ___________
            ___         /       ___ 
      1   \/ 5         /  5   \/ 5  
x95 = - + ----- - I*  /   - - ----- 
      4     4       \/    8     8   

$$x_{95} = \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$

                         ___________
            ___         /       ___ 
      1   \/ 5         /  5   \/ 5  
x96 = - + ----- + I*  /   - - ----- 
      4     4       \/    8     8   

$$x_{96} = \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$

                           ___________
              ___         /       ___ 
        1   \/ 5         /  5   \/ 5  
x97 = - - - ----- - I*  /   - - ----- 
        4     4       \/    8     8   

$$x_{97} = - \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$

                           ___________
              ___         /       ___ 
        1   \/ 5         /  5   \/ 5  
x98 = - - - ----- + I*  /   - - ----- 
        4     4       \/    8     8   

$$x_{98} = - \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}$$

                         ___________
            ___         /       ___ 
      1   \/ 5         /  5   \/ 5  
x99 = - - ----- - I*  /   - + ----- 
      4     4       \/    8     8   

$$x_{99} = - \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$

                          ___________
             ___         /       ___ 
       1   \/ 5         /  5   \/ 5  
x100 = - - ----- + I*  /   - + ----- 
       4     4       \/    8     8   

$$x_{100} = - \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}$$

Численный ответ

x1 = 0.968583161128631 - 0.248689887164855*i

x2 = 0.770513242775789 + 0.63742398974869*i

x3 = -0.992114701314478 - 0.125333233564304*i

x4 = 0.998026728428272 + 0.0627905195293134*i

x5 = 0.187381314585725 - 0.982287250728689*i

x6 = 0.982287250728689 - 0.187381314585725*i

x7 = 0.535826794978997 - 0.844327925502015*i

x8 = 0.248689887164855 - 0.968583161128631*i

x9 = -0.951056516295154 - 0.309016994374947*i

x10 = 0.309016994374947 - 0.951056516295154*i

x11 = -0.728968627421412 - 0.684547105928689*i

x12 = -0.63742398974869 + 0.770513242775789*i

x13 = -0.929776485888251 + 0.368124552684678*i

x14 = -0.187381314585725 - 0.982287250728689*i

x15 = 1.0*i

x16 = -0.309016994374947 - 0.951056516295154*i

x17 = -0.0627905195293134 - 0.998026728428272*i

x18 = 0.951056516295154 + 0.309016994374947*i

x19 = -0.309016994374947 + 0.951056516295154*i

x20 = -0.982287250728689 - 0.187381314585725*i

x21 = -0.187381314585725 + 0.982287250728689*i

x22 = 0.968583161128631 + 0.248689887164855*i

x23 = 0.876306680043864 + 0.481753674101715*i

x24 = 0.876306680043864 - 0.481753674101715*i

x25 = -0.968583161128631 + 0.248689887164855*i

x26 = 0.248689887164855 + 0.968583161128631*i

x27 = 0.481753674101715 - 0.876306680043864*i

x28 = 0.587785252292473 + 0.809016994374947*i

x29 = -0.951056516295154 + 0.309016994374947*i

x30 = 0.809016994374947 - 0.587785252292473*i

x31 = -0.968583161128631 - 0.248689887164855*i

x32 = -0.992114701314478 + 0.125333233564304*i

x33 = -0.844327925502015 - 0.535826794978997*i

x34 = -0.481753674101715 - 0.876306680043864*i

x35 = 0.90482705246602 + 0.425779291565073*i

x36 = -1.0*i

x37 = 0.125333233564304 + 0.992114701314478*i

x38 = -0.90482705246602 + 0.425779291565073*i

x39 = 0.929776485888251 - 0.368124552684678*i

x40 = 0.368124552684678 - 0.929776485888251*i

x41 = 0.844327925502015 + 0.535826794978997*i

x42 = 0.368124552684678 + 0.929776485888251*i

x43 = 0.187381314585725 + 0.982287250728689*i

x44 = 0.728968627421412 - 0.684547105928689*i

x45 = -0.876306680043864 - 0.481753674101715*i

x46 = 0.844327925502015 - 0.535826794978997*i

x47 = 0.992114701314478 + 0.125333233564304*i

x48 = -0.368124552684678 + 0.929776485888251*i

x49 = -0.63742398974869 - 0.770513242775789*i

x50 = 0.63742398974869 - 0.770513242775789*i

x51 = 0.0627905195293134 + 0.998026728428272*i

x52 = -0.998026728428272 + 0.0627905195293134*i

x53 = 0.587785252292473 - 0.809016994374947*i

x54 = 0.684547105928689 + 0.728968627421412*i

x55 = 1.0

x56 = -0.998026728428272 - 0.0627905195293134*i

x57 = -0.125333233564304 + 0.992114701314478*i

x58 = 0.0627905195293134 - 0.998026728428272*i

x59 = -0.684547105928689 - 0.728968627421412*i

x60 = -0.481753674101715 + 0.876306680043864*i

x61 = 0.90482705246602 - 0.425779291565073*i

x62 = 0.125333233564304 - 0.992114701314478*i

x63 = -0.809016994374947 - 0.587785252292473*i

x64 = 0.982287250728689 + 0.187381314585725*i

x65 = -0.125333233564304 - 0.992114701314478*i

x66 = 0.63742398974869 + 0.770513242775789*i

x67 = -0.809016994374947 + 0.587785252292473*i

x68 = -0.929776485888251 - 0.368124552684678*i

x69 = -0.770513242775789 - 0.63742398974869*i

x70 = 0.992114701314478 - 0.125333233564304*i

x71 = -0.587785252292473 - 0.809016994374947*i

x72 = 0.728968627421412 + 0.684547105928689*i

x73 = 0.951056516295154 - 0.309016994374947*i

x74 = 0.770513242775789 - 0.63742398974869*i

x75 = 0.309016994374947 + 0.951056516295154*i

x76 = -0.90482705246602 - 0.425779291565073*i

x77 = -0.684547105928689 + 0.728968627421412*i

x78 = 0.684547105928689 - 0.728968627421412*i

x79 = 0.929776485888251 + 0.368124552684678*i

x80 = 0.425779291565073 + 0.90482705246602*i

x81 = -0.535826794978997 + 0.844327925502015*i

x82 = 0.809016994374947 + 0.587785252292473*i

x83 = 0.998026728428272 - 0.0627905195293134*i

x84 = -0.248689887164855 + 0.968583161128631*i

x85 = -0.587785252292473 + 0.809016994374947*i

x86 = 0.481753674101715 + 0.876306680043864*i

x87 = -0.425779291565073 - 0.90482705246602*i

x88 = -0.770513242775789 + 0.63742398974869*i

x89 = 0.535826794978997 + 0.844327925502015*i

x90 = -0.535826794978997 - 0.844327925502015*i

x91 = -0.728968627421412 + 0.684547105928689*i

x92 = -0.982287250728689 + 0.187381314585725*i

x93 = -0.425779291565073 + 0.90482705246602*i

x94 = -0.0627905195293134 + 0.998026728428272*i

x95 = -0.248689887164855 - 0.968583161128631*i

x96 = -0.368124552684678 - 0.929776485888251*i

x97 = -0.844327925502015 + 0.535826794978997*i

x98 = -0.876306680043864 + 0.481753674101715*i

x99 = 0.425779291565073 - 0.90482705246602*i

x100 = -1.0

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