[Math] Solving complex equation, $z^4 = (z + 1)^4$

Question

We just started learning about complex numbers, and I'm having some trouble on how to solve this problem.
$$z^4 = (z + 1)^4$$

Was wondering if anyone could help me out.

Answer 1

$(z+1)^4-z^4=((z+1)^2+z^2)((z+1)^2-z^2)=(2z^2+2z+1)(2z+1)$, which gives the answer: $$\left\{-\frac{1}{2}-\frac{1}{2}i,-\frac{1}{2}+\frac{1}{2}i,-\frac{1}{2}\right\}$$