Find the Fourth Roots Of $\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } i$

Multiple Choice

Find the fourth roots of $\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } i$ . Write the roots in trigonometric form.

A)
$\begin{array} { l } w _ { 1 } = \cos \left( 65 ^ { \circ } \right) + i \sin \left( 65 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 155 ^ { \circ } \right) + i \sin \left( 155 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 245 ^ { \circ } \right) + i \sin \left( 245 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 335 ^ { \circ } \right) + i \sin \left( 335 ^ { \circ } \right) \end{array}$
B)
$\begin{array} { l } w _ { 1 } = \cos \left( 75 ^ { \circ } \right) + i \sin \left( 75 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 165 ^ { \circ } \right) + i \sin \left( 165 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 255 ^ { \circ } \right) + i \sin \left( 255 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 345 ^ { \circ } \right) + i \sin \left( 345 ^ { \circ } \right) \end{array}$
C)
$\begin{array} { l } w _ { 1 } = \cos \left( 80 ^ { \circ } \right) + i \sin \left( 80 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 170 ^ { \circ } \right) + i \sin \left( 170 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 260 ^ { \circ } \right) + i \sin \left( 260 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 350 ^ { \circ } \right) + i \sin \left( 350 ^ { \circ } \right) \end{array}$
D)
$\begin{array} { l } w _ { 1 } = \cos \left( 70 ^ { \circ } \right) + i \sin \left( 70 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 160 ^ { \circ } \right) + i \sin \left( 160 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 250 ^ { \circ } \right) + i \sin \left( 250 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 340 ^ { \circ } \right) + i \sin \left( 340 ^ { \circ } \right) \end{array}$
E)
$\begin{array} { l } w _ { 1 } = \cos \left( 85 ^ { \circ } \right) + i \sin \left( 85 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 175 ^ { \circ } \right) + i \sin \left( 175 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 265 ^ { \circ } \right) + i \sin \left( 265 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 355 ^ { \circ } \right) + i \sin \left( 355 ^ { \circ } \right) \end{array}$