 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/11/b/ii/solution

\frac{1}{z} = \frac{x - i y}{x ^{2} + y ^{2}} .

Therefore, away from the origin,

Re (1/ z) = \frac{x}{x ^{2} + y ^{2}}, Im (1/ z) = - \frac{y}{x ^{2} + y ^{2}} .

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