\begin{definition}[Definition:Dot Product/Complex/Definition 1]
Let $z_1 := x_1 + i y_1$ and $z_2 := x_2 + i y_2$ be complex numbers.
The '''dot product''' of $z_1$ and $z_2$ is defined as:
:$z_1 \circ z_2 = x_1 x_2 + y_1 y_2$
\end{definition}