Definition:Dot Product/Complex/Definition 1

Definition

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:

$z_1 \circ z_2 = x_1 x_2 + y_1 y_2$

Also see

• Equivalence of Definitions of Complex Dot Product

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Dot and Cross Product