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

$\overline{z}+\mathrm{z}=0$
$\Rightarrow \overline{z}=-\mathrm{z}$…………(1)
$\text{ Now }|\mathrm{z}{|}^2-4\mathrm{zi}={\mathrm{z}}^2$
$\Rightarrow -{\mathrm{z}}^2-4\mathrm{zi}={\mathrm{z}}^2$     [from (1)]
$\begin{array}{l}\Rightarrow 2\mathrm{z}=-4\mathrm{i}\\ \Rightarrow \mathrm{z}=-2\mathrm{i}\\ \Rightarrow \left|\mathrm{z}\right|=2\end{array}$