 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-1/11/d/i/solution

For arbitrary complex

b

and real

c

z z^{*} + b z^{*} + b^{*} z + c = ∣ z + b ∣^{2} + c - ∣ b ∣^{2} .

The locus is a single point exactly when

c = ∣ b ∣^{2}, z = - b .

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