 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/iii/solution

Use

∣ z ∣^{2} = z \overset{z}{ˉ}

and

z - \overset{z}{ˉ} = 2 i y

. Then

\overset{z}{ˉ} (z^{2} - ∣ z ∣^{2}) = \overset{z}{ˉ} z (z - \overset{z}{ˉ}) = 2 i y ∣ z ∣^{2} = 2 i y (x^{2} + y^{2}) .

0 and 2 y (x^{2} + y^{2}), respectively .

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