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

Example of Complex Dot Product

Let:

$z_1 = 2 + 5 i$

$z_2 = 3 - i$

Then:

$\size {z_1 \circ z_2} = 1$

where:

$\circ$ denotes (complex) dot product

$\size {\, \cdot \,}$ denotes the absolute value function.

Proof

\(\ds z_1 \circ z_2\)

\(=\)

\(\ds 1\)

Complex Dot Product: $2 + 5 i \circ 3 - i$

\(\ds \leadsto \ \ \)

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

\(=\)

\(\ds \size 1\)

\(\ds \)

\(=\)

\(\ds 1\)

$\blacksquare$

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