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:

$z_1 \times z_2 := \map \Im {\overline {z_1} z_2}$

where:

$\map \Im z$ 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

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Dot and Cross Product