Solve the equation:$ \bar{z}=z^{n-1}$ Solve the following equation:
$\bar{z}=z^{n-1}$
Where $\bar{z}$ is the complex conjugate of z, and n is a natural number such that $n\neq 2$.
I have tried to write z in rectangular form and polar form. I have tried to play with De Moivre's formula. 
But I still do not see where to proceed from here.
Could you please point me to the right direction?
Thanks.

Use polar coordinates, $z = re^{i\theta}$:
$$re^{-i\theta} = r^{n-1}e^{i(n-1)\theta},$$
$$r = r^{n-1}\implies\cdots,$$
$$\cdots$$
