# Product of Complex Numbers in Polar Form/Examples/3 cis 40 x 4 cis 80

## Example of Use of Product of Complex Numbers in Polar Form

$3 \cis 40 \degrees \times 4 \cis 80 \degrees = -6 + 6 \sqrt 3 i$

## Proof

 $\ds 3 \cis 40 \degrees \times 4 \cis 80 \degrees$ $=$ $\ds \paren {3 \times 4} \map \cis {40 \degrees + 80 \degrees}$ Product of Complex Numbers in Polar Form $\ds$ $=$ $\ds 12 \cis 120 \degrees$ $\ds$ $=$ $\ds 12 \paren {\cos 120 \degrees + i \sin 120 \degrees}$ $\ds$ $=$ $\ds 12 \times \paren {-\dfrac 1 2} + 12 i \paren {\dfrac {\sqrt 3} 2}$ Cosine of $120 \degrees$, Sine of $120 \degrees$ $\ds$ $=$ $\ds -6 + 6 \sqrt 3 i$ simplifying

$\blacksquare$