Complex Cross Product/Examples/Size of 3-i cross 2+5i

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Example of Complex Cross Product

Let:

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

Then:

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

where:

$\circ$ denotes (complex) cross product
$\size {\, \cdot \,}$ denotes the absolute value function.


Proof

\(\displaystyle z_1 \times z_2\) \(=\) \(\displaystyle 17\) Complex Cross Product: $3 - i \times 2 + 5 i$
\(\displaystyle \leadsto \ \ \) \(\displaystyle \size {z_1 \times z_2}\) \(=\) \(\displaystyle \size {17}\)
\(\displaystyle \) \(=\) \(\displaystyle 17\)

$\blacksquare$


Sources