Complex numbers problem I'm trying to use the relevant rules and definitions but making little progress.


Assume $z=a+bi$ and $a,b\in\mathbb{R^+}$:
$$z\left(1+z^{*}\right)+\frac{5\Im\left(iz\right)}{1-2i}-2\Re\left(z^{*}\right)-4=0\Longleftrightarrow$$
$$z\left(1+z^{*}\right)-(1-2i)\Re(z)-4=0\Longleftrightarrow$$
$$zz^{*}-(1-2i)\Re(z)+z-4=0$$
