Write Complex Numbers in Polar Form
-$$- 3 - 4 i$$
A) $5 \left( \cos 233.1 ^ { \circ } + i \sin 233.1 ^ { \circ } \right)$
B) $5 \left( \cos 306.9 ^ { \circ } + i \sin 306.9 ^ { \circ } \right)$
C) $5 \left( \cos 126.9 ^ { \circ } + i \sin 126.9 ^ { \circ } \right)$
D) $5 \left( \cos 53.1 ^ { \circ } + \mathrm { i } \sin 53.1 ^ { \circ } \right)$ Write the complex number in polar form. Express the argument in radians.

Question

Quizplus · Accepted Answer

The magnitude $r$ of the complex number $-3 - 4i$ is $\sqrt{(-3)^2 + (-4)^2} = 5$. The argument $\theta$, measured in degrees, is found by $\tan^{-1}\left(\frac{-4}{-3}\right)$, which gives $53.1^\circ$. However, since the complex number is in the third quadrant, we add $180^\circ$ to $53.1^\circ$ to get $233.1^\circ$. Therefore, the polar form is $5(\cos 233.1^\circ + i\sin 233.1^\circ)$.

Write Complex Numbers in Polar Form - −3−4i- 3 - 4 i−3−4i

Write Complex Numbers in Polar Form
- $- 3 - 4 i$