# Definition:Dot Product/Complex/Definition 3

## Definition

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

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

$z_1 \circ z_2 := \map \Re {\overline {z_1} z_2}$

where:

$\map \Re z$ denotes the real part of a complex number $z$
$\overline {z_1}$ denotes the complex conjugate of $z_1$
$\overline {z_1} z_2$ denotes complex multiplication.