Where z is a complex number in the form $z = a+bi$, and $n\in \mathbb{R}$. I was capable of solving this for $z^2 = z^\ast$ by expanding both sides. But I was wondering if there was a way to solve for all n.
The answers I got for $z^2 = z^\ast$ were: $$ z= 0$$ $$ z= 1$$ $$ z= -\frac{1}{2} + \frac{\sqrt3}{2}i$$ $$ z= -\frac{1}{2} - \frac{\sqrt3}{2}i$$