 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/10/b/iii/solution

i

rotates the plane counterclockwise through

π /2

. The center

3 + 2 i

maps to

- 2 + 3 i

, while distances are preserved. Thus the locus is a circle centered at $(- 2, 3)$ with radius eight:

(X + 2)^{2} + (Y - 3)^{2} = 64.

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