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

Question

Quizplus · Accepted Answer

The complex number $\sqrt{3} - i$ can be converted to polar form using the formula $r(\cos \theta + i\sin \theta)$, where $r = \sqrt{a^2 + b^2}$ and $\theta = \tan^{-1}\left(\frac{b}{a}\right)$. Here, $a = \sqrt{3}$ and $b = -1$, so $r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2$, and $\theta = \tan^{-1}\left(\frac{-1}{\sqrt{3}}\right) = -30^\circ$. Since we typically express the angle in a range from 0 to 360 degrees for polar form, we add 360 degrees to -30 degrees to get 330 degrees. Therefore, the polar form is $2(\cos 330^\circ + i\sin 330^\circ)$.

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

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