\begin{definition}[Definition:Dot Product/Complex/Definition 3]
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.
\end{definition}