Write the complex number in rectangular form.
-$$6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$$
A) $- 3 \sqrt { 3 } - 3 i$
B) $- 3 \sqrt { 3 } + 3 i$
C) $3 \sqrt { 3 } - 3 \mathrm { i }$
D) $3 \sqrt { 3 } + 3 \mathrm { i }$

Question

Quizplus · Accepted Answer

The complex number in rectangular form is obtained by converting the polar form $r(\cos \theta + i\sin \theta)$ to $x + yi$, where $x = r\cos \theta$ and $y = r\sin \theta$. For $\theta = 330^\circ$, $\cos 330^\circ = \sqrt{3}/2$ and $\sin 330^\circ = -1/2$. Thus, $x = 6(\sqrt{3}/2) = 3\sqrt{3}$ and $y = 6(-1/2) = -3$, making the rectangular form $3\sqrt{3} - 3i$.

Write the Complex Number in Rectangular Form 6(cos⁡330∘+isin⁡330∘)6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)6(cos330∘+isin330∘)

Write the Complex Number in Rectangular Form $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$