📂Complex Anaylsis

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.

See Also

• Sign of real numbers