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$4z^2+8|z|^2-3=0$

I have to find $z$.

$|z|^2 = z\cdot \bar{z}$, but I don't know if this helps in this situation.

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You can prove first that $z^2$ is real, and then use the fact that $|z|^2=|z^2|$.

Can you find $z^2$ then?

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    Answers: $z = \pm\frac12, \pm i\frac{\sqrt{3}}{2}$ (after corrections)2013-04-05