1. The problem statement, all variables and given/known data Consider the equation (z-1)^23 = z^23 Show that all solutions lie on the line Re(z)=1/2 How many solutions are there 2. Relevant equations 3. The attempt at a solution Really have no idea. I figured polar form might be helpful somehow so I converted it and got (r(cos (theta) + isin (theta)) - 1)^23 - r^23(cos (23*theta) + isin (23*theta))=0 I'm getting hung up on the first term. I'm not really sure what I can do with it.