 Solution

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

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

w = lo g ∣ z ∣ + i (ar g z + 2 πn), n \in Z .

Because

x > 0

, one may take the complex argument

ar g z = arctan (y / x)

. Consequently

Re w = \frac{1}{2} lo g (x^{2} + y^{2}), Im w = arctan \frac{y}{x} + 2 πn, q u a d n \in Z .

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