Complex Cross Product is Anticommutative/Examples/2+5i cross 3-i
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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:
- $\paren {2 + 5 i} \times \paren {3 - i} = -\paren {\paren {3 - i} \times \paren {2 + 5 i} }$
$\blacksquare$