## Trigonometry (11th Edition) Clone

$27i$
De Moivre’s Theorem states that when $r (\cos\theta+i \sin\theta)$ is a complex number, and if $n$ is any real number, then the following relationship holds. $[ r (\cos\theta+i \sin\theta)]^{n}=[ r^{n} (\cos n\theta+i \sin n\theta)]$ In compact form, this is written $[ r cis\theta]^{n}=[ r^{n} (cis \theta)]$ $[ 3 (\cos 30^{\circ}+i \sin30^{\circ})]^{3}=[ 3^{3} (\cos 3\times30^{\circ}+i \sin 3\times30^{\circ})]$ $=[ 27 (\cos 90^{\circ}+i \sin 90^{\circ})]$ $=[ 27 (0+i.1]$ $=27i$