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if |z^2-1|=|z|^2+1 then z lies on...

if `|z^2-1|=|z|^2+1` then `z` lies on

A

a circle

B

a parabola

C

an ellipse

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Let `z=x+iy`. Then,
`|z^(2)-1|=|z|^(2)+1`
`rArr |(x^(2)-y^(2)-1)+2ixy|=x^(2)+y^(2)+1`
`rArr (x^(2)-y^(2)-1)^(2)+4x^(2)y^(2)=(x^(2)+y^(2)+1)^(2)`
`rArr x=0`
`rArr` z lies on imaginary axis.
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