Definition:Vector Cross Product/Complex/Definition 3

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

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


 * $z_1 \times z_2 := \operatorname{Im} \left({\overline {z_1} z_2}\right)$

where:
 * $\operatorname{Im} \left({z}\right)$ denotes the imaginary part of a complex number $z$
 * $\overline {z_1}$ denotes the complex conjugate of $z_1$
 * $\overline {z_1} z_2$ denotes complex multiplication.

Also see

 * Equivalence of Definitions of Complex Cross Product