Complex equation solution. How can i resolve it? I have this complex equation $|z+2i|=| z-2 |$. How can i resolve it? Please help me

We have $|z+2i|^2=| z-2 |^2$, which implies that
$(z+2i)\overline{(z+2i)}=(z-2)\overline{(z-2)}$, that is
$(z+2i)(\overline{z}-2i)=(z-2)(\overline{z}-2)$. This implies that
$$z\overline{z}-2iz+2i\overline{z}+4=z\overline{z}-2z-2\overline{z}+4,$$
that is
$-iz+i\overline{z}=-z-\overline{z}$, or 
$$i(z-\overline{z})=z+\overline{z}.$$
Now if we write $z=a+bi$, we get
$i(2bi)=2a$, or $b=-a$.
