1.

if `|z^2-1|=|z|^2+1` then `z` lies onA. a circleB. a parabolaC. an ellipseD. none of these

Answer» Correct Answer - 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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