This is another "challenge question" from my book on complex analysis. I didn't really get why the points outlined below the question text would work, but I tried to follow them anyway to see what would happen.
I've attached the question text and my progress with this so far. Since z = 1 and z = -1 are obvious roots, I start by dividing by z^2 - 1. Then I think I've gotten to the point where I've solved the bi-quadratic equation for u, but I can't figure out how to get from there to a solution for z.
Thanks for any help!