Q.

The number of complex numbers z such that |z−i|=|z+i|=|z+1| is

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a

0

b

1

c

2

d

infinite

answer is B.

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Detailed Solution

TIP Note z is circum-centre of the circle passing through three non-collinear points A(0+i),B(0−i)andC(−1+0i)Thus, there is only one value of z.
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The number of complex numbers z such that |z−i|=|z+i|=|z+1| is