a) Find all \(z\) such that \((z+1)^7 = z^7.\)

You should write down all the solutions explicitly, but they don't need to be in either rectangular or exponential form.

b) Prove that all the solutions to the above equation have equal real parts, and find what this real part is equal to.

I don't necessarily need at an answer, but an explanation would be greatly appreciated, thank you!

Guest Jun 12, 2021