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
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.