Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 2 / 8

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- Solution 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)

.

Figure 1.
Circle in the complex plane with centre one and radius two
. Details.

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