Write the complex number in trigonometric form $$r ( \cos \theta + i \sin \theta )$$ with θ in the interval [0°, 360°).
-$3 \sqrt { 3 } - 3 i$
A) $6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$
B) $6 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
C) $6 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$
D) $6 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The complex number $3 \sqrt { 3 } - 3 i$ can be written in trigonometric form as $$r ( \cos \theta + i \sin \theta ) = 6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$$where $r = \sqrt { ( 3 \sqrt { 3 } ) ^ { 2 } + ( - 3 ) ^ { 2 } } = 6$ and $\theta = \tan ^ { - 1 } \left( \frac { - 3 } { 3 \sqrt { 3 } } \right) = 330 ^ { \circ }$.

Write the Complex Number in Trigonometric Form r(cos⁡θ+isin⁡θ)r ( \cos \theta + i \sin \theta )r(cosθ+isinθ)

Write the Complex Number in Trigonometric Form $r ( \cos \theta + i \sin \theta )$