Q.

The number of complex numbers satisfying the equation |z|=2  and |z|=|z−1|  is

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a

0

b

1

c

2

d

infinite

answer is C.

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Detailed Solution

|z|=|z−1|  represent the straight z=1/2. This line meets the circle |z|=2  in exactly two points viz. 12±152i.
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The number of complex numbers satisfying the equation |z|=2  and |z|=|z−1|  is