 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/i/solution

∣ z + b ∣^{2} = ∣ b ∣^{2} - c .

For

∣ b ∣^{2} > c

, this is the circle with centre

- b

∣ b ∣^{2} - c

. Equality gives just the point

- b

, and

∣ b ∣^{2} < c

gives the empty locus. In particular, the nondegenerate answer is

centre - b, radius ∣ b ∣^{2} - c .

 New to topics? Read the docs here!