\begin{definition}[Definition:Dot Product/Complex/Definition 4]
Let $z_1$ and $z_2$ be complex numbers.
The '''dot product''' of $z_1$ and $z_2$ is defined as:
:$z_1 \circ z_2 := \dfrac {\overline {z_1} z_2 + z_1 \overline {z_2} } 2$
where:
:$\overline {z_1}$ denotes the complex conjugate of $z_1$
:$\overline {z_1} z_2$ denotes complex multiplication.
\end{definition}