Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary.
-$\sqrt { 3 } - i$
A) $2 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right)$
B) $2 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$
C) $4 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$
D) $4 \left( \cos 330 ^ { \circ } + \mathrm { i } \sin 330 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The magnitude $r$ of the complex number $\sqrt{3} - i$ is $\sqrt{(\sqrt{3})^2 + (-1)^2} = \sqrt{3 + 1} = 2$. The argument $\theta$, in degrees, is found by $\tan^{-1}\left(\frac{-1}{\sqrt{3}}\right)$, which gives $-30^\circ$. Since the complex number is in the fourth quadrant, we add $360^\circ$ to get $330^\circ$. Thus, the polar form is $2(\cos 330^\circ + i\sin 330^\circ)$.

Write the Complex Number in Polar Form 3−i\sqrt { 3 } - i3​−i

Write the Complex Number in Polar Form $\sqrt { 3 } - i$