Use De Moivre's theorem to evaluate $(\cos 30^\circ + i\sin 30^\circ)^6$.
A$1$
B$\cos 30^\circ + i\sin 30^\circ$
C$-1$CORRECT
D$i$
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Why the answer is C, and why the others tempt you.
De Moivre's theorem gives $(\cos\theta + i\sin\theta)^n = \cos n\theta + i\sin n\theta$. With $n = 6$ and $\theta = 30^\circ$: $\cos 180^\circ + i\sin 180^\circ = -1 + 0i = -1$. Expanding by the binomial theorem gives the same result but is far longer.
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