 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/ii/solution

With

z_{1} = a + ib

and

z_{2} = c + i d

, direct multiplication gives

z_{1} z_{2} = (a c - b d) + i (a d + b c)

. Taking the complex conjugate yields

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

 New to topics? Read the docs here!