How to express this function in closed form without condition verfication and Re and Im functions (only with absolute value function)?
$f(z)= \begin{cases} - \operatorname{sgn}(\operatorname{Im}(z)), & \mbox{if } \operatorname{Re}(x)=0 \\ \operatorname{sgn}(\operatorname{Re}(z)), & \mbox{if } \operatorname{Re}(x)\ne 0 \end{cases}$