 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/b/iv/solution

There is a single point exactly when the radius is zero:

c = ∣ b ∣^{2}, z = - b .

Then

∣ z + b ∣^{2} = 0

forces this unique value of the complex number

z

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