$\def\Arg{\operatorname{Arg}}$I have here a complex equation:
$z^2-\Arg(z)=z\overline z, \qquad z\in \mathbb C$
where $\Arg(z)$ is the argument of $z$, and $\overline z$ is complex conjugate of $z$.
How do we get the solutions of this equation? I started replacing $z=x+iy$ but I can't continue. Any suggestions please?