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# If $\mid z^2-1\mid=\mid z\mid^2+1$ then $z$ lies on

$\begin{array}{1 1}(A)Circle \\ (B) The\;imaginary\;axis\\ (C) The\;real\;axis \\(D) None\;of\;these \end{array}$

$\mid z^2-1\mid=\mid z\mid^2+1$
$\mid z^2+(-1)\mid=\mid z\mid^2+\mid-1\mid$
$\iff\large\frac{z^2}{-1}$ is non-negative real no
$\iff z^2$ is non-positive real no
$\iff z$ lies on imaginary axis.
Hence (B) is the correct answer.
edited Jun 7, 2014