Complex Dot Product/Examples/3-i dot 2+5i
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Examples of Complex Dot Product
Let:
- $z_1 = 3 - i$
- $z_1 = 2 + 5 i$
Then:
- $z_1 \circ z_2 = 1$
where $\circ$ denotes (complex) dot product.
Proof
\(\ds z_1 \circ z_2\) | \(=\) | \(\ds \paren {3 - i} \circ \paren {2 + 5 i}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 2 + \paren {-1} \times 5\) | 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: $110 \ \text {(c)}$