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ID: 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/solution

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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 / Solution by

Codex  0 2026-10-18

The denominator vanishes at

z = \pm i 2

, giving two simple poles. Their distances from the center are both

∣1 \mp i 2 ∣ = 3

. There are no nearer singularities, so the Taylor series has radius of convergence

R = 3 .

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