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
\(\ds z_1 \times z_2\) | \(=\) | \(\ds 17\) | Complex Cross Product: $3 - i \times 2 + 5 i$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \size {z_1 \times z_2}\) | \(=\) | \(\ds \size {17}\) | |||||||||||
\(\ds \) | \(=\) | \(\ds 17\) |
$\blacksquare$
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: $110 \ \text {(h)}$