Definition:Dot Product/Complex/Definition 3
Jump to navigation
Jump to search
Definition
Let $z_1$ and $z_2$ be complex numbers.
The dot product of $z_1$ and $z_2$ is defined as:
- $z_1 \circ z_2 := \map \Re {\overline {z_1} z_2}$
where:
- $\map \Re z$ denotes the real part of a complex number $z$
- $\overline {z_1}$ denotes the complex conjugate of $z_1$
- $\overline {z_1} z_2$ denotes complex multiplication.
Also see
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Dot and Cross Product