Let f be a holomorphic function in the open unit disk D = {z ∈ C: |z| < 1} such that f(0) = 0 and |f(z)| ≤ 1 for all z in D. Now, consider another function g defined as g(z) = zf'(z) - f(z) for all z in D. If for a specific z = z₀ in D with z₀ ≠ 0, we have |f(z0)| = |z0|, which of the following statements is true?
1
g(z₀) = f'(z₀) for all z₀ ≠ 0 in D
2
g(z) = 0 for all z in D
3
|g(z₀)| ≥ 1
4
|g(z₀)| ≤ 1