Solve complex numbers

Question

Pls help me to solve this equation on photo enter image description here

Answer 1

Hint: As $z=1$ is not a solution of $$(z+1)^n+(z-1)^n=0$$ you can reewrite the equation as $$\biggl(\frac{z+1}{z-1}\biggr)^{\!n}=-1=\mathrm e^{i\pi}$$ Solve for $u^n=-1$ first, then express $z$ in function of $u$.