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

Question

Quizplus · Accepted Answer

The given expression is in the form of Euler's formula, $e^{i\theta} = \cos\theta + i\sin\theta$, where $\theta = 30^\circ$. Raising it to the 12th power, we use the identity $e^{i\theta n} = (\cos\theta + i\sin\theta)^n$, where $n = 12$ and $\theta = 30^\circ$. This simplifies to $e^{i360^\circ}$, which equals 1 in rectangular form, since $\cos(360^\circ) = 1$ and $\sin(360^\circ) = 0$.

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