Answer
$27i$
Work Step by Step
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
$[ r cis\theta]^{n}=[ r^{n} (cis \theta)]$
$[ 3 (\cos 30^{\circ}+i \sin30^{\circ})]^{3}=[ 3^{3} (\cos 3\times30^{\circ}+i \sin 3\times30^{\circ})]$
$=[ 27 (\cos 90^{\circ}+i \sin 90^{\circ})]$
$=[ 27 (0+i.1]$
$=27i$
