Answer
$8$
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
$[ r cis\theta]^{n}=[ r^{n} (cis \theta)]$
$[2 (\cos 120^{\circ}+i \sin 120^{\circ})]^{3}=[ (8\cos 3\times 120^{\circ}+i \sin 3\times 120^{\circ})]$
$=[ 8(\cos 360^{\circ}+i \sin 360^{\circ})]$
$=8(1+i.0)$
$=8$
