Find the given power. Write answer in rectangular form.
-$$\left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) ^{12}$$
A) 1
B) -i
C) i
D) -1

Question

Quizplus · Accepted Answer

Using De Moivre's Theorem, $(\cos \theta + i \sin \theta)^n = \cos(n\theta) + i \sin(n\theta)$. Here, $n=12$ and $\theta=30^\circ$, so $n\theta = 360^\circ$. Thus, $\cos(360^\circ) + i \sin(360^\circ) = 1 + i(0) = 1$.

Find the Given Power (cos⁡30∘+isin⁡30∘)12\left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) ^{12}(cos30∘+isin30∘)12

Find the Given Power $\left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) ^{12}$