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If `|z^2-1|=|z|^2+1`, then `z` lies on (a) a circle (b) the imaginary axis (c) the real axis (d) an ellipse

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If `|z^2-1|=|z|^2+1`, then `z` lies on (a) a circle (b) the imaginary axis (c) the real axis (d) an ellipse
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`|Z^2-1|=|Z^2|-1`
`|(Z^2-1)^2|=(|Z^2|-1)^2`
`(Z^2-1)(Z^2-1)=(1+ZZ)^2`
`-(Z^2-2^2)=2*Z*Z`
Re(Z)=0
Z lies on the imaginary axis.
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