Complex Cross Product is Anticommutative/Examples/2+5i cross 3-i

Example of Use of Complex Cross Product is Anticommutative

Example: $\paren {2 + 5 i} \times \paren {3 - i}$

Let:

$z_1 = 2 + 5 i$

$z_2 = 3 - i$

Then:

$z_1 \times z_2 = -17$

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

Example: $\paren {3 - i} \times \paren {2 + 5 i}$

Let:

$z_1 = 3 - i$

$z_2 = 2 + 5 i$

Then:

$z_1 \times z_2 = 17$

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

As can be seen:

$\paren {2 + 5 i} \times \paren {3 - i} = -\paren {\paren {3 - i} \times \paren {2 + 5 i} }$

$\blacksquare$