If `|z^2-1|=|z|^2+1`, then `z` lies on(a) a circle(b) the imaginary ax – InterviewSolution

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1.	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
Answer» `\|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)=2ZZ` Re(Z)=0 Z lies on the imaginary axis.

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