 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/11/11-2c/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

ζ = R e^{i θ}

x = \frac{c}{2} (R + R^{- 1}) cos θ

and

y = \frac{c}{2} (R - R^{- 1}) sin θ

. Thus

a = c (R + R^{- 1}) /2

b = c (R - R^{- 1}) /2

. Nested level curves and the behaviour at infinity show that exteriors correspond.

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