Write the complex number in trigonometric form $$r ( \cos \theta + i \sin \theta )$$ with θ in the interval [0°, 360°).
-$4 \sqrt { 3 } + 4 i$
A) $8 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$
B) $8 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
C) $8 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
D) $8 \left( \cos 150 ^ { \circ } + \mathrm { i } \sin 150 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The magnitude $r$ of the complex number $4\sqrt{3} + 4i$ is $r = \sqrt{(4\sqrt{3})^2 + 4^2} = \sqrt{48 + 16} = \sqrt{64} = 8$. The angle $\theta$ can be found using the tangent, which is $\tan(\theta) = \frac{4}{4\sqrt{3}} = \frac{1}{\sqrt{3}}$, leading to $\theta = 30^\circ$. Therefore, the complex number in trigonometric form is $8(\cos 30^\circ + i\sin 30^\circ)$.

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 $r ( \cos \theta + i \sin \theta )$