Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2023 / Paper 1 / 7 / d / i

The denominator vanishes at $z=\pm i\sqrt{2}$, giving two simple poles. Their distances from the center are both $|1\mp i\sqrt{2}|=\sqrt{3}$. There are no nearer singularities, so the Taylor series has radius of convergence