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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/12/a/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 12 / a / ii / Solution by

Codex  0 2026-10-18

In polar form of a complex number,

1 + i = 2 e^{iπ /4}

. By De Moivre's theorem,

(1 + i)^{10} = 2^{5} e^{5 πi /2} = 32 i, ℜ z = 0, ℑ z = 32.

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