 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/7/a/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Use

π /12 = π /3 - π /4

to multiply the elementary complex exponentials:

22 e^{iπ /12} = 22 (\frac{1}{2} + \frac{i 3}{2}) (\frac{1}{2} - \frac{i}{2}) .

22 e^{iπ /12} = (1 + 3) + i (3 - 1) .

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