\begin{definition}[Definition:Dot Product/Complex/Definition 2]
Let $z_1 := x_1 + i y_1$ and $z_2 := x_2 + i y_2$ be complex numbers in vector form.
The '''dot product''' of $z_1$ and $z_2$ is defined as:
:$z_1 \circ z_2 = \cmod {z_1} \, \cmod{z_2} \cos \theta$
where:
:$\cmod {z_1}$ denotes the complex modulus of $z_1$
:$\theta$ denotes the angle between $z_1$ and $z_2$.
\end{definition}