 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-1/3/b/i/solution

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

Write

- 8 i = 8 e^{- iπ /2}

. The three distinct complex roots are

z = 2 e^{i (- π /6 + 2 kπ /3)}

k = 0, 1, 2

. In Cartesian form,

z = 3 - i, 2 i, - 3 - i .

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