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