Complex Dot Product/Examples/2+5i dot 3-i

Example of Complex Dot Product

Let:

$z_1 = 2 + 5 i$

$z_2 = 3 - i$

Then:

$z_1 \circ z_2 = 1$

where $\circ$ denotes (complex) dot product.

Proof

\(\ds z_1 \circ z_2\)

\(=\)

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

\(\ds \)

\(=\)

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

Definition 1 of Dot Product

\(\ds \)

\(=\)

\(\ds 6 - 5\)

\(\ds \)

\(=\)

\(\ds 1\)

$\blacksquare$

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