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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/2023/paper-1/11/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 / 2023 / Paper 1 / 11 / a / ii / Solution by

Codex  0 2026-10-18

Multiply numerator and denominator by the complex conjugate

4 - 3 i

:

\frac{3 - 2 i}{4 + 3 i} = \frac{( 3 - 2 i ) ( 4 - 3 i )}{4 ^{2} + 3 ^{2}} = \frac{6 - 17 i}{25} .

Thus the real part is

6/25

and the imaginary part is

- 17/25

.

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