Let f be a non-constant entire function such that |f(z)| = 1 for |z| = 1.
Let U denote the open unit disk around 0.
Which of the following is FALSE?
1
f(ℂ) = ℂ
2
f has at least one zero in U
3
f has at most finitely many distinct zeros in ℂ
4
f can have a zero outside U
5
Question Not Attempted