 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/11/a/i/solution

Write

z_{1} = a + ib

and

z_{2} = c + i d

with real

a, b, c, d

(z_{1} + z_{2})^{*} = [(a + c) + i (b + d)]^{*} = (a + c) - i (b + d) = (a - ib) + (c - i d) = z_{1}^{*} + z_{2}^{*} .

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