x=sqrt(a) (уравнение)

Найду корень уравнения: x=sqrt(a)

Вы ввели

      ___
x = \/ a 

$$x = \sqrt{a}$$

Быстрый ответ

        _________________                                 _________________                         
     4 /   2        2        /atan2(im(a), re(a))\     4 /   2        2        /atan2(im(a), re(a))\
x1 = \/  im (a) + re (a) *cos|-------------------| + I*\/  im (a) + re (a) *sin|-------------------|
                             \         2         /                             \         2         /

$$x_{1} = i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$

Сумма и произведение корней

сумма

   _________________                                 _________________                         
4 /   2        2        /atan2(im(a), re(a))\     4 /   2        2        /atan2(im(a), re(a))\
\/  im (a) + re (a) *cos|-------------------| + I*\/  im (a) + re (a) *sin|-------------------|
                        \         2         /                             \         2         /

$$i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$

=

   _________________                                 _________________                         
4 /   2        2        /atan2(im(a), re(a))\     4 /   2        2        /atan2(im(a), re(a))\
\/  im (a) + re (a) *cos|-------------------| + I*\/  im (a) + re (a) *sin|-------------------|
                        \         2         /                             \         2         /

$$i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$

произведение

   _________________                                 _________________                         
4 /   2        2        /atan2(im(a), re(a))\     4 /   2        2        /atan2(im(a), re(a))\
\/  im (a) + re (a) *cos|-------------------| + I*\/  im (a) + re (a) *sin|-------------------|
                        \         2         /                             \         2         /

$$i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$

=

                      I*atan2(im(a), re(a))
   _________________  ---------------------
4 /   2        2                2          
\/  im (a) + re (a) *e                     

$$\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} e^{\frac{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2}}$$