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If |z^2-1|=|z|^2+1, then z lies on (a) ...

If `|z^2-1|=|z|^2+1`, then `z` lies on (a) The Real axis (b)The imaginary axis (c)A circle (d)An ellipse

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=z+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`
Hence, z lies on imaginary axis.
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