# complex variable!

$-\mid(-Z)\mid$ should give +Z while $-\mid-Z\mid$ should give -Z
If $|u|$ denotes the absolute value of $u$, then $-|(-z)|$ and $-|{-z}|$ are the same expression, and it is not true that $-|{-z}|=z$ or $-|{-z}|=-z$ for all complex $z$.