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

Example of Complex Cross Product

Let:

$z_1 = 2 + 5 i$

$z_2 = 3 - i$

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: $2 + 5 i \times 3 - i$

\(\ds \leadsto \ \ \)

\(\ds \size {z_1 \times z_2}\)

\(=\)

\(\ds \size {-17}\)

\(\ds \)

\(=\)

\(\ds 17\)

$\blacksquare$

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