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Question

The locus of z in the argand diagram is the circle |z| = 2, then show that the locus of |z+1| is circle with centre (1,0) and radius 2.

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Solution

Let
z=2eiθ
=2cosθ+i2sinθ
Hence
z+1
=1+2cosθ+i2sinθ
=x+iy
Then
x1=2cosθ
y=2sinθ
Hence
(x1)2+y2=4
Hence z+1 is the equation of a circle centered at (1,0) with radius equal to 2.

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