 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-1/1b/b/i/solution

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

ω = e^{2 πi /3} = - \frac{1}{2} + \frac{3}{2} i,

1 + ω = \frac{1}{2} + \frac{3}{2} i = e^{iπ /3} .

Therefore

(1 + ω)^{10} = e^{10 πi /3} = e^{4 πi /3} = - \frac{1}{2} - \frac{3}{2} i .

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