 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/14/a/i/solution

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

Thus

ℜ z = \frac{12}{13}, ℑ z = \frac{5}{13} .

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