Definition:Dot Product/Complex/Definition 2
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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:
- $z_1 \circ z_2 = \cmod {z_1} \, \cmod{z_2} \cos \theta$
where:
- $\cmod {z_1}$ denotes the complex modulus of $z_1$
- $\theta$ denotes the angle between $z_1$ and $z_2$.
Also see
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Dot and Cross Product