X^2+y^2-8x+12y+52=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Suma y producto de raíces
[src]
4 + I*(-6 - re(y)) + im(y) + 4 - im(y) + I*(6 + re(y))
$$\left(i \left(- \operatorname{re}{\left(y\right)} - 6\right) + \operatorname{im}{\left(y\right)} + 4\right) + \left(i \left(\operatorname{re}{\left(y\right)} + 6\right) - \operatorname{im}{\left(y\right)} + 4\right)$$
8 + I*(-6 - re(y)) + I*(6 + re(y))
$$i \left(- \operatorname{re}{\left(y\right)} - 6\right) + i \left(\operatorname{re}{\left(y\right)} + 6\right) + 8$$
(4 + I*(-6 - re(y)) + im(y))*(4 - im(y) + I*(6 + re(y)))
$$\left(i \left(- \operatorname{re}{\left(y\right)} - 6\right) + \operatorname{im}{\left(y\right)} + 4\right) \left(i \left(\operatorname{re}{\left(y\right)} + 6\right) - \operatorname{im}{\left(y\right)} + 4\right)$$
(4 - im(y) + I*(6 + re(y)))*(4 - I*(6 + re(y)) + im(y))
$$\left(- i \left(\operatorname{re}{\left(y\right)} + 6\right) + \operatorname{im}{\left(y\right)} + 4\right) \left(i \left(\operatorname{re}{\left(y\right)} + 6\right) - \operatorname{im}{\left(y\right)} + 4\right)$$
(4 - im(y) + i*(6 + re(y)))*(4 - i*(6 + re(y)) + im(y))
x1 = 4 + I*(-6 - re(y)) + im(y)
$$x_{1} = i \left(- \operatorname{re}{\left(y\right)} - 6\right) + \operatorname{im}{\left(y\right)} + 4$$
x2 = 4 - im(y) + I*(6 + re(y))
$$x_{2} = i \left(\operatorname{re}{\left(y\right)} + 6\right) - \operatorname{im}{\left(y\right)} + 4$$
x2 = i*(re(y) + 6) - im(y) + 4