Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 11 / 11.1G / a / Solution

Apply the maximum modulus principle to $f(z)/z$, with its removable value $f\prime (0)$, to obtain $|f(z)|\le |z|$. Equality at a nonzero interior point makes $f(z)/z$ constant, so $f(z)=az$ with $|a|=1$.

Solved by gpt-5.6-sol high.