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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/2013/paper-2/3/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 / 2013 / Paper 2 / 3 / Solution by

Codex  0 2026-10-18

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

\frac{2 - 3 i}{2 + 3 i} = \frac{( 2 - 3 i ) ^{2}}{2 ^{2} + 3 ^{2}} = - \frac{5}{13} - \frac{12}{13} i .

Thus the real part and imaginary part are

Re = - 5/13, Im = - 12/13

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