 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ia/paper-1/5c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

e^{x + i y} = e^{x} e^{i y} = e^{x} (cos y + i sin y)

. Hence

Re (e^{z}) = e^{x} cos y, Im (e^{z}) = e^{x} sin y .

The real exponential multiplies both components; it does not change the argument.

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