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

Example of Complex Cross Product

Let:

$z_1 = 2 + 5 i$

$z_2 = 3 - i$

Then:

$z_1 \times z_2 = -17$

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

Proof

\(\ds z_1 \circ z_2\)

\(=\)

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

\(\ds \)

\(=\)

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

Definition 1 of Complex Cross Product

\(\ds \)

\(=\)

\(\ds -2 - 15\)

\(\ds \)

\(=\)

\(\ds -17\)

$\blacksquare$

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: $110 \ \text {(b)}$