I have been racking my brain about the following for an hour now, to no avail… Can anyone help out, or at least tell me the first couple of steps in resolving this?
$z$ is a complex number and $n \geq 1$ is a natural number. It is given that |z|=2. Calculate the number $α=|z^n+\overline z^n|^2+|z^n-\overline z^n|^2$.
Thank you!