 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/11/c/i/solution

Under the given rotation,

\overset{z}{ˉ} = \overset{α}{ˉ} \overset{w}{ˉ}

and

z \overset{z}{ˉ} = ∣ α ∣^{2} w \overset{w}{ˉ} = w \overset{w}{ˉ}

. Collecting terms gives

a w \overset{w}{ˉ} + b \overset{α}{ˉ} \overset{w}{ˉ} + \overset{ˉ}{b} α w + c = 0.

Since

\overline{b \overset{α}{ˉ}} = \overset{ˉ}{b} α

, the transformed coefficients are

A = a, B = b \overset{α}{ˉ}, C = c .

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