I've tried two ways, but get stuck.
I've tried to simplify, but didn't know what to do next, and I've tried to solve it like a Quadratic equation but got stuck too.
One way got me this:
$$\frac{z}{2} \times (-1+3i+z)-1-i=0$$ – don't know what next.
option b, got me mess, while trying to make the equation into a Quadratic.
Best Answer
Using the quadratic formula for a general quadratic $ax^2+bx+c=0$ which is $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=0$$ for $z^2-(1-3i)z-2i-2=0$ $$z=\frac{1-3i\pm \sqrt{-8-6i+8i+8}}{2}$$ $$\implies z=\frac{1-3i\pm \sqrt{2i}}{2}$$