Answer
-1
Work Step by Step
Using de Moivre's theorem ($z^{n}=r^{n} cis \,n\theta$ where $z=r\, cis\,\theta$ and $n$ is an integer), we get
$(cis\,18^{\circ})^{10}=[1(\cos 18^{\circ}+i\sin 18^{\circ})]^{10}$
$=(1)^{10}(\cos 10\cdot18^{\circ}+i\sin 10\cdot18^{\circ})$
$=\cos 180^{\circ}+i\sin180^{\circ}$
In standard form, our result is
$=-1+i\cdot0$
$=-1$
