1. The problem statement, all variables and given/known data Let z be a complex number such that z^n=(z+1)^n=1. Show that n|6 (n divides 6) and that z^3=1. 2. Relevant equations n|6 → n=1,2,3,6 3. The attempt at a solution The z+1, I think, is what throws me off. Considering z^n=1 by itself, for even n, z=±1 and for odd n, z=1. The (z+1) term, however, contradicts this result and leaves me right back where i started. How should I begin looking at this?