 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ia/paper-1/1c/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Since

z \overline{z} = ∣ z ∣^{2} = x^{2} + y^{2}

\frac{1}{z} - \frac{1}{z} = \frac{z - z}{∣ z ∣ ^{2}} = - \frac{2 i y}{x ^{2} + y ^{2}} .

Therefore

Re = 0, Im = - \frac{2 y}{x ^{2} + y ^{2}} .

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