The product of the four values of $\left[\cos \left(\frac{\pi}{3}\right)+i \sin \left(\frac{\pi}{3}\

Question

The product of the four values of $\left[\cos \left(\frac{\pi}{3}\right)+i \sin \left(\frac{\pi}{3}\right)^{\frac{3}{4}}\right]$ is

Professor PC Thomas Classes · Answer

Leveraging De Moivre's principles, root tracking produces identically $1$ upon product consolidation.