Dot Product Operator is Commutative/Examples/2+5i dot 3-i

Example of Use of Dot Product Operator is Commutative

Example: $\paren {2 + 5 i} \circ \paren {3 - i}$

Let:

$z_1 = 2 + 5 i$

$z_2 = 3 - i$

Then:

$z_1 \circ z_2 = 1$

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

Example: $\paren {3 - i} \circ \paren {2 + 5 i}$

Let:

$z_1 = 3 - i$

$z_1 = 2 + 5 i$

Then:

$z_1 \circ z_2 = 1$

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

As can be seen:

$\paren {2 + 5 i} \circ \paren {3 - i} = \paren {3 - i} \circ \paren {2 + 5 i}$

$\blacksquare$