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## Homework Statement

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

## Homework Equations

## 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.