# How do you use DeMoivre's Theorem to simplify (2(cos(pi/2)+isin(pi/2)))^8?

${\left(2 \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)\right)}^{8} = 256$
${\left(2 \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)\right)}^{8} = {2}^{8} \left(\cos \left(8 \cdot \frac{\pi}{2}\right) + i \sin \left(8 \cdot \frac{\pi}{2}\right)\right)$.
${2}^{8} \left(\cos \left(8 \cdot \frac{\pi}{2}\right) + i \sin \left(8 \cdot \frac{\pi}{2}\right)\right) = 256 \left(\cos \left(4 \pi\right) + i \sin \left(4 \pi\right)\right) = 256 \left(1 + i \cdot 0\right) = 256$