 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/1a/a/i/solution

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

\frac{a z + b}{z + 1} = z ⟺ z^{2} + (1 - a) z - b = 0.

A unique solution at

z = i

(z - i)^{2} = z^{2} - 2 i z - 1.

Comparing coefficients gives

a = 1 + 2 i, b = 1 .

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