 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-3/3b/a/solution

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

Taking the complex derivative along the real direction gives

f^{'} (z) = u_{x} + i v_{x} .

Taking it along the imaginary direction and equating the two expressions gives the Cauchy-Riemann equations

u_{x} = v_{y}, u_{y} = - v_{x} .

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