The Sign of Complex Numbers
Definition 1 2
The sign of a complex number $\lambda \in \mathbb{C}$ is defined as follows. $$ \operatorname{sign} ( \lambda ) = \begin{cases} \displaystyle {{ \lambda } \over { \left| \lambda \right| }} &, \lambda \ne 0 \\ 0 &, \lambda = 0 \end{cases} $$
Description
As an easily checkable example, the sign of real numbers $\operatorname{sign} ( +2 ) = 1$, $\operatorname{sign} ( -3 ) = -1$ can be immediately verified. Thus, in terms of generalization of reals, it is a sufficiently good definition.