 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-2/8/solution

Write

z = x + i y

. The complex modulus condition is equivalent to

(x - 1)^{2} + y^{2} = 4

. Thus the locus is a circle of radius two centred at $(1, 0)$ in the complex plane. Its extreme points are

(- 1, 0)

(3, 0)

, and

(1, \pm 2)

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