Suma y producto de raíces
[src]
3 / 3 \
re (x) |im (x) 2 | 2 2 2
- ------ + I*|------ - re (x)*im(x)| + im (x)*re(x) + -1 + re (x) - im (x) + 2*I*im(x)*re(x)
3 \ 3 /
$$\left(i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) + \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)$$
3 / 3 \
2 2 re (x) |im (x) 2 | 2
-1 + re (x) - im (x) - ------ + I*|------ - re (x)*im(x)| + im (x)*re(x) + 2*I*im(x)*re(x)
3 \ 3 /
$$i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \left(\operatorname{re}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1$$
/ 3 / 3 \ \
| re (x) |im (x) 2 | 2 | / 2 2 \
|- ------ + I*|------ - re (x)*im(x)| + im (x)*re(x)|*\-1 + re (x) - im (x) + 2*I*im(x)*re(x)/
\ 3 \ 3 / /
$$\left(i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)$$
/ 3 2 / 2 2 \ \ / 2 2 \
-\re (x) - 3*im (x)*re(x) + I*\- im (x) + 3*re (x)/*im(x)/*\-1 + re (x) - im (x) + 2*I*im(x)*re(x)/
----------------------------------------------------------------------------------------------------
3
$$- \frac{\left(i \left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(x\right)} + \left(\operatorname{re}{\left(x\right)}\right)^{3} - 3 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)}{3}$$
-(re(x)^3 - 3*im(x)^2*re(x) + i*(-im(x)^2 + 3*re(x)^2)*im(x))*(-1 + re(x)^2 - im(x)^2 + 2*i*im(x)*re(x))/3
3 / 3 \
re (x) |im (x) 2 | 2
y1 = - ------ + I*|------ - re (x)*im(x)| + im (x)*re(x)
3 \ 3 /
$$y_{1} = i \left(- \left(\operatorname{re}{\left(x\right)}\right)^{2} \operatorname{im}{\left(x\right)} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{3}}{3}\right) - \frac{\left(\operatorname{re}{\left(x\right)}\right)^{3}}{3} + \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2}$$
2 2
y2 = -1 + re (x) - im (x) + 2*I*im(x)*re(x)
$$y_{2} = \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 i \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1$$
y2 = re(x)^2 + 2*i*re(x)*im(x) - im(x)^2 - 1