# Definition:Vector Cross Product/Complex/Definition 4

## Definition

Let $z_1$ and $z_2$ be complex numbers.

The cross product of $z_1$ and $z_2$ is defined as:

$z_1 \times z_2 := \dfrac {\overline {z_1} z_2 - z_1 \overline {z_2}} {2 i}$

where:

$\overline {z_1}$ denotes the complex conjugate of $z_1$
$\overline {z_1} z_2$ denotes complex multiplication.