Q.

If a complex number z  lies on a circle of radius 1/2,having center at origin then  complex number (−1+4z)  lies on a circle of radius:

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a

1/2

b

1

c

2

d

4

answer is C.

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Detailed Solution

Let           |z|=1/2 Let        z1=−1+4z ∴              z=z1+14 From Eq. (i),    |z1+14|=1/2⇒|z1+1|=2 .
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If a complex number z  lies on a circle of radius 1/2,having center at origin then  complex number (−1+4z)  lies on a circle of radius: