]> 18.4 De Moivre's Theorem

## 18.4 De Moivre's Theorem

The variable $z , z = x + i y$ can be represented by its length and angle as can any two dimensional vector, and the relation as usual is

$r 2 = x 2 + y 2$
and
$x = r cos ⁡ θ , y = r sin ⁡ θ$

De Moivre's Theorem is the statement that $e θ = cos ⁡ θ + i sin ⁡ θ$ . We can therefore write

$z = x + i y = r e i θ$