 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/4/solution

\frac{2 + 3 i}{4 - 5 i} = \frac{( 2 + 3 i ) ( 4 + 5 i )}{4 ^{2} + 5 ^{2}} = \frac{- 7 + 22 i}{41} .

Thus the real part and imaginary part are respectively

- \frac{7}{41}, \frac{22}{41} .

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