Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 11 / 11.2C / i / Solution

Off the slit choose the stated analytic square-root branch. Differentiation gives $f\prime (z)=c^{-1}(1+z/\sqrt{z^2-c^2})$, which does not vanish there, so the map is conformal.

Solved by gpt-5.6-sol high.