Absolute Value of Complex Cross Product is Commutative/Examples/2+5i cross 3-i

Example of Use of Absolute Value of Complex Cross Product is Commutative

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

Let:

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

Then:

$\size {z_1 \times z_2} = 17$

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

Let:

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

Then:

$\size {z_1 \times z_2} = 17$

As can be seen:

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

$\blacksquare$