# Solving complex equations

Suppose the equation $(E):z^2-2\sin(\alpha)z+2(1+\cos(\alpha))=0$ / $z\in \mathbb{C}$.

I tried to calculate the discriminant but I could determinate it's sign(there is a hint $\Im (z_{1})\ge \Im(z_{2})$ / $z_{2}$ and $z_{1}$ are the two solution of the equation.

In a second case we suppose $(E_{2}):z^3-(1+i\sqrt{3})z^2-2(1+i\sqrt{3})z-4+4i\sqrt{3}$.

In this case I can't use the formula of solving the Cubic polynomial and I know it has two solutions.

So the question is how can I solve those equations?

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