Write the complex number in trigonometric form $$r ( \cos \theta + i \sin \theta )$$ with θ in the interval [0°, 360°).
-$- 12 - 16 i$
A) $20 \left( \cos 126.9 ^ { \circ } + i \sin 126.9 ^ { \circ } \right)$
B) $20 \left( \cos 53.1 ^ { \circ } + i \sin 53.1 ^ { \circ } \right)$
C) $20 \left( \cos 306.9 ^ { \circ } + i \sin 306.9 ^ { \circ } \right)$
D) $20 \left( \cos 233.1 ^ { \circ } + i \sin 233.1 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The complex number $-12 - 16i$ is in the third quadrant. The modulus is $r = \sqrt{(-12)^2 + (-16)^2} = 20$, and the argument $\theta$ is $\tan^{-1}(\frac{-16}{-12}) = 53.1^\circ$. Since it's in the third quadrant, $\theta = 180^\circ + 53.1^\circ = 233.1^\circ$.

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