Write the complex number in rectangular form.
-$3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$
A) $\frac { \sqrt { 3 } } { 2 } + \frac { 3 \sqrt { 3 } } { 2 }$ i
B) $\frac { \sqrt { 3 } } { 6 } + \frac { \sqrt { 3 } } { 6 } \mathrm { i }$
C) $\sqrt { 3 } + i$
D) $\frac { 3 } { 2 } + \frac { 3 \sqrt { 3 } } { 2 } \mathrm { i }$

Question

Quizplus · Accepted Answer

The complex number in rectangular form is obtained by evaluating the trigonometric expressions: $\cos \frac{\pi}{3} = \frac{1}{2}$ and $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}$. Multiplying these by 3 gives $3 \times \frac{1}{2} = \frac{3}{2}$ and $3 \times \frac{\sqrt{3}}{2} = \frac{3\sqrt{3}}{2}$, resulting in $\frac{3}{2} + \frac{3\sqrt{3}}{2}i$.

Write the Complex Number in Rectangular Form 3(cos⁡π3+isin⁡π3)3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)3(cos3π​+isin3π​)

Write the Complex Number in Rectangular Form $3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$