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

Example of Complex Cross Product

Let:

$z_1 = 3 - i$

$z_2 = 2 + 5 i$

Then:

$z_1 \times z_2 = 17$

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

Proof

\(\ds z_1 \circ z_2\)

\(=\)

\(\ds \paren {3 - i} \times \paren {2 + 5 i}\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren 5 - \paren {-1} \times 2\)

Definition 1 of Complex Cross Product

\(\ds \)

\(=\)

\(\ds 15 - \paren {-2}\)

\(\ds \)

\(=\)

\(\ds 17\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: The Dot and Cross Product: $110 \ \text {(d)}$