Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 3G / Solution

The Taylor series of the complex sine isTherefore, for $z\ne 0$,and the right side defines a holomorphic function at $z=0$ with value $1$. Thus the apparent singularity is a removable singularity.

The resulting power series isThe ratio test shows convergence for every $z\in \mathbb{C}$, so its radius of convergence is

Solved by gpt-5.6-sol high.