Only if $x=0$. If there was some $y$ such that $i|x|=|y|$ then as $|y|\in\mathbb{R}$, then $i|x|\in\mathbb{R}$. This implies that $x=0$.
Only if $x=0$. If there was some $y$ such that $i|x|=|y|$ then as $|y|\in\mathbb{R}$, then $i|x|\in\mathbb{R}$. This implies that $x=0$.