Suma y producto de raíces
[src]
_________________ _________________ _________________ _________________
4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\
- \/ im (x) + re (x) *cos|-------------------| - I*\/ im (x) + re (x) *sin|-------------------| + \/ im (x) + re (x) *cos|-------------------| + I*\/ im (x) + re (x) *sin|-------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right)$$
$$0$$
/ _________________ _________________ \ / _________________ _________________ \
| 4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\| |4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\|
|- \/ im (x) + re (x) *cos|-------------------| - I*\/ im (x) + re (x) *sin|-------------------||*|\/ im (x) + re (x) *cos|-------------------| + I*\/ im (x) + re (x) *sin|-------------------||
\ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}\right)$$
_________________
/ 2 2 I*atan2(im(x), re(x))
-\/ im (x) + re (x) *e
$$- \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}$$
-sqrt(im(x)^2 + re(x)^2)*exp(i*atan2(im(x), re(x)))
_________________ _________________
4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\
y1 = - \/ im (x) + re (x) *cos|-------------------| - I*\/ im (x) + re (x) *sin|-------------------|
\ 2 / \ 2 /
$$y_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}$$
_________________ _________________
4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\
y2 = \/ im (x) + re (x) *cos|-------------------| + I*\/ im (x) + re (x) *sin|-------------------|
\ 2 / \ 2 /
$$y_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}$$
y2 = i*(re(x)^2 + im(x)^2)^(1/4)*sin(atan2(im(x, re(x))/2) + (re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2))