Consider the function f which is holomorphic in the open unit disk D = {z ∈ C: |z| < 1} and satisfies the condition f(0) = 0. Suppose there exists an α ∈ D for which |f(α)| = |α|. Which of the following is correct?
1
f(z) maintains the property |f(z)| ≤ |z| for every z ∈ D
2
f(z) maintains the property |f(z)| ≥ |z| for every z ∈ D
3
f(z) can only be represented by the function φz for some φ ∈ D
4
None of these