Write the complex number in rectangular form.
-$$8 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$$
A) $\frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i }$
B) $4 \sqrt { 3 } + 4 \mathrm { i }$
C) $\frac { \sqrt { 3 } } { 4 } + \frac { 1 } { 4 } \mathrm { i }$
D) $4 + 4 \sqrt { 3 } \mathrm { i }$

Question

Quizplus · Accepted Answer

The complex number in rectangular form is obtained by multiplying the magnitude (8) by the cosine and sine values. For $\frac{\pi}{6}$, $\cos\frac{\pi}{6} = \sqrt{3}/2$ and $\sin\frac{\pi}{6} = 1/2$. Thus, $8(\cos\frac{\pi}{6} + i\sin\frac{\pi}{6}) = 8(\sqrt{3}/2 + i/2) = 4\sqrt{3} + 4i$.

Write the Complex Number in Rectangular Form 8(cos⁡π6+isin⁡π6)8 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)8(cos6π​+isin6π​)

Write the Complex Number in Rectangular Form $8 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$