Definition:Dot Product/Complex/Definition 2

Definition
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:


 * $z_1 \circ z_2 = \left\vert{z_1}\right\vert \, \left\vert{z_2}\right\vert \cos \theta$

where:
 * $\left\vert{z_1}\right\vert$ denotes the complex modulus of $z_1$
 * $\theta$ denotes the angle between $z_1$ and $z_2$.

Also see

 * Equivalence of Definitions of Complex Dot Product