Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 12 / 12.2A / a / Solution

For distinct $z,w$ in the convex disc, integrate along the segment:The second term has modulus strictly below $|f^{\prime }(z_0)||z-w|$, so the sum cannot vanish. Thus $f$ is one-to-one.

Solved by gpt-5.6-sol high.