Question

Let $z$ be a complex number, and let $n$ be a positive integer such that\[z^n = (z + 1)^n = 1.\]
a) Prove that $|z| = |z+1| = 1$.
b) Find the possible values of $z$ in exponential form.
c) Prove that $n$ must be divisible by $6$.

Answer 1

B) Find the possible values of $z$ in exponential forms