# Complex Cross Product/Examples/3-4i cross -4+3i/Proof 2

## Examples of Complex Cross Product

Let:

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

Then:

$z_1 \times z_2 = -7$

where $\times$ denotes (complex) cross product.

## Proof

 $\ds z_1 \circ z_2$ $=$ $\ds \paren {3 - 4 i} \times \paren {-4 + 3 i}$ $\ds$ $=$ $\ds 3 \times 3 - \paren {-4} \times \paren {-4}$ Definition 1 of Complex Cross Product $\ds$ $=$ $\ds 9 - 16$ $\ds$ $=$ $\ds -7$

$\blacksquare$