I have this problem, I need to show that it's true and I don't have a clue.
I tried to do like alpha = x+yi but it got me nowhere, any ideas?
It is defined for , this is because .
Therefore, on the closed disk the function is a continous function that is analytic on the open disk . By the maximum modulos theorem theorem the largest value that attains happens on the boundary of the disk i.e. on .
We know that , therefore, if we have:
Therefore, for all and furthermore if and only if .