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

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

$\blacksquare$