Complex Dot Product/Examples/Size of 3-i dot 2+5i

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Example of Complex Dot Product

Let:

$z_1 = 3 - i$
$z_2 = 2 + 5 i$

Then:

$\size {z_1 \circ z_2} = 1$

where:

$\circ$ denotes (complex) dot product
$\size {\, \cdot \,}$ denotes the absolute value function.


Proof

\(\ds z_1 \circ z_2\) \(=\) \(\ds 1\) Complex Dot Product: $3 - i \circ 2 + 5 i$
\(\ds \leadsto \ \ \) \(\ds \size {z_1 \circ z_2}\) \(=\) \(\ds \size 1\)
\(\ds \) \(=\) \(\ds 1\)

$\blacksquare$


Sources