 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/12/b/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

1 + z

. For

z \neq = - 1

this gives

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

Thus its real part and imaginary part are respectively

\frac{1 - x ^{2} - y ^{2}}{( 1 + x ) ^{2} + y ^{2}}, \frac{- 2 y}{( 1 + x ) ^{2} + y ^{2}} .

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