# Complex Dot Product/Examples

## Examples of Complex Dot Product

### Example: $\paren {3 - 4 i} \circ \paren {-4 + 3 i}$

Let:

$z_1 = 3 - 4 i$
$z_2 = -4 + 3 i$

Then:

$z_1 \circ z_2 = -24$

where $\circ$ denotes (complex) dot product.

### Acute Angle Between $\paren {3 - 4 i}$ and $\paren {-4 + 3 i}$

Consider:

$z_1 = 3 - 4 i$
$z_2 = -4 + 3 i$

expressed as vectors.

Then the acute angle between $z_1$ and $z_2$ is approximately $16 \degrees 16'$