I need to draw the set of all complex numbers, which satisfy the following inequality:
$|z^2| > Im(z)^2$
This is what I've already done:
$|z^2| > Im(z)^2$
$|z|^2 > Im(z)^2$ - use $z = a + ib$
$\sqrt{a^2 + b^2}^2 > b^2$
$a^2 + b^2 > b^2$
$a^2 > 0$
$a \neq 0$
Is it correct, that the inequality describes the set of all complex numbers except the ones without a real-value - plotted everything except the imaginary axis?