I have a task: Prove that if for each complex number u,w,z we have: $uwz=1$ and $u+w+z=u^{-1}+w^{-1}+z^{-1}$ then at least one of them is equal 1. I tried substituting $u=(uw)^{-1}$ to the second equality and prove that by denying, but I can't solve it. Thanks in advance. Login To add answer/comment