Sign of Complex Numbers
Definition12
For a complex number $\lambda \in \mathbb{C}$, the sign is defined as follows. $$ \operatorname{sign} ( \lambda ) = \begin{cases} \displaystyle {{ \lambda } \over { \left| \lambda \right| }} &, \lambda \ne 0 \\ 0 &, \lambda = 0 \end{cases} $$
Explanation
As an example that can be easily checked, one can immediately verify the signs of real numbers $\operatorname{sign} ( +2 ) = 1$ and $\operatorname{sign} ( -3 ) = -1$. Therefore, as a generalization of the real case, it is a sufficiently good definition.