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If $|z^{2} - 1| = |z^{2}| + 1,$ then $z$ is lies on

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Correct option is B

z2-1=z2+1 can be written as z2+(−1)=z2+-1 ⇔ z2-1 is a non-negative real number. ⇔ z2 is a non-positive real number. ⇔ z lies on the imaginary axis.

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If z2-1=z2+1, then z is lies on

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If $|z^{2} - 1| = |z^{2}| + 1,$ then $z$ is lies on