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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/i/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 / i / Solution by

Codex  0 2026-10-18

Multiply numerator and denominator by the complex conjugate of the denominator:

\frac{2 + i}{- 1 + i} = \frac{( 2 + i ) ( - 1 - i )}{2} = \frac{- 1 - 3 i}{2} .

Squaring gives

(- 1 - 3 i)^{2} /4 = (- 8 + 6 i) /4

. Thus the real part and imaginary part are

ℜ z = - 2, ℑ z = \frac{3}{2} .

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