Complex numbers - Exponential numbers - Proof Let $z$ be a complex number, and let $n$ be a positive integer such that $z^n = (z + 1)^n = 1$. Prove that $n$ is divisible by 6.
For this problem I am stumped...how should I begin?
Also there's a hint for it:
From $z^n = 1$, prove that $|z| = 1$. What does the equation $(z + 1)^n = 1$ tell you? What do the resulting equations tell you about $z$?
Could someone give me a hint on where to begin? thanks in advance

Hint 1: $|z-z_0|=r$ is a circle with radius $r$ and center $z_0$;
Hint 2: the unit circle is $z=e^{i\theta}$;
Hint 3: for any $n\in\Bbb{N}$,   $(e^{i\theta})^n=e^{in\theta}$;
Hint 4: if $\cos \theta= \pm 1$ and $\sin \theta =0$ then $\theta=k\pi$ for some integer $k$;
Hint 5: if $a,b,c$ are integers such that $a|bc$ and $\gcd(a,b)=1$ then $a|c$.
