Question

Modulus of nonzero complex number z satisfying $\overline{z}+z=0$ and ${\left|z\right|}^2-4zi=z^2$ is

Answer 1

given that $\overline{z}+z=0$
and ${\left|z\right|}^2-4zi=z^2$
$\Rightarrow z\overline{z}-4zi=-z\overline{z}$
$\Rightarrow 2z\overline{z}=4zi$
Since, $z\ne 0$
Therefore, $\overline{z}=2i$
$\Rightarrow \left|z\right|=2$
Ans: 2