Suma y producto de raíces
[src]
2
/ _________________ \ _________________ _________________ / _________________ \
| 4 / 2 2 /atan2(im(a), re(a))\| / 2 2 2/atan2(im(a), re(a))\ 4 / 2 2 | 4 / 2 2 /atan2(im(a), re(a))\| /atan2(im(a), re(a))\
|4 + \/ im (a) + re (a) *cos|-------------------|| - \/ im (a) + re (a) *sin |-------------------| + 2*I*\/ im (a) + re (a) *|4 + \/ im (a) + re (a) *cos|-------------------||*sin|-------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$
2
/ _________________ \ _________________ _________________ / _________________ \
| 4 / 2 2 /atan2(im(a), re(a))\| / 2 2 2/atan2(im(a), re(a))\ 4 / 2 2 | 4 / 2 2 /atan2(im(a), re(a))\| /atan2(im(a), re(a))\
|4 + \/ im (a) + re (a) *cos|-------------------|| - \/ im (a) + re (a) *sin |-------------------| + 2*I*\/ im (a) + re (a) *|4 + \/ im (a) + re (a) *cos|-------------------||*sin|-------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$
2
/ _________________ \ _________________ _________________ / _________________ \
| 4 / 2 2 /atan2(im(a), re(a))\| / 2 2 2/atan2(im(a), re(a))\ 4 / 2 2 | 4 / 2 2 /atan2(im(a), re(a))\| /atan2(im(a), re(a))\
|4 + \/ im (a) + re (a) *cos|-------------------|| - \/ im (a) + re (a) *sin |-------------------| + 2*I*\/ im (a) + re (a) *|4 + \/ im (a) + re (a) *cos|-------------------||*sin|-------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$
_________________ _________________
4 / 2 2 /atan2(im(a), re(a))\ 4 / 2 2 /atan2(im(a), re(a))\
16 + I*im(a) + 8*\/ im (a) + re (a) *cos|-------------------| + 8*I*\/ im (a) + re (a) *sin|-------------------| + re(a)
\ 2 / \ 2 /
$$8 i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 8 \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} + 16$$
16 + i*im(a) + 8*(im(a)^2 + re(a)^2)^(1/4)*cos(atan2(im(a), re(a))/2) + 8*i*(im(a)^2 + re(a)^2)^(1/4)*sin(atan2(im(a), re(a))/2) + re(a)
2
/ _________________ \ _________________ _________________ / _________________ \
| 4 / 2 2 /atan2(im(a), re(a))\| / 2 2 2/atan2(im(a), re(a))\ 4 / 2 2 | 4 / 2 2 /atan2(im(a), re(a))\| /atan2(im(a), re(a))\
x1 = |4 + \/ im (a) + re (a) *cos|-------------------|| - \/ im (a) + re (a) *sin |-------------------| + 2*I*\/ im (a) + re (a) *|4 + \/ im (a) + re (a) *cos|-------------------||*sin|-------------------|
\ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$x_{1} = \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right)^{2} + 2 i \left(\sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} + 4\right) \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(a\right)},\operatorname{re}{\left(a\right)} \right)}}{2} \right)}$$
x1 = ((re(a)^2 + im(a)^2)^(1/4)*cos(atan2(im(a, re(a))/2) + 4)^2 + 2*i*((re(a)^2 + im(a)^2)^(1/4)*cos(atan2(im(a), re(a))/2) + 4)*(re(a)^2 + im(a)^2)^(1/4)*sin(atan2(im(a), re(a))/2) - sqrt(re(a)^2 + im(a)^2)*sin(atan2(im(a), re(a))/2)^2)