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( 50 ^ { \circ } \right) + i \sin \left( 50 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 140 ^ { \circ } \right) + i \sin \left( 140 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 230 ^ { \circ } \right) + i \sin \left( 230 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 320 ^ { \circ } \right) + i \sin \left( 320 ^ { \circ } \right)\end{array}

B)

\begin{array} { l } w _ { 1 } = \cos \left( 60 ^ { \circ } \right) + i \sin \left( 60 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 150 ^ { \circ } \right) + i \sin \left( 150 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 240 ^ { \circ } \right) + i \sin \left( 240 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 330 ^ { \circ } \right) + i \sin \left( 330 ^ { \circ } \right)\end{array}

C)

\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}

D)

\begin{array} { l } w _ { 1 } = \cos \left( 55 ^ { \circ } \right) + i \sin \left( 55 ^ { \circ } \right) \\w _ { 2 } = \cos \left( 145 ^ { \circ } \right) + i \sin \left( 145 ^ { \circ } \right) \\w _ { 3 } = \cos \left( 235 ^ { \circ } \right) + i \sin \left( 235 ^ { \circ } \right) \\w _ { 4 } = \cos \left( 325 ^ { \circ } \right) + i \sin \left( 325 ^ { \circ } \right)\end{array}

E)

\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}

Determine Whether u\mathbf { u }u And v\mathbf { v }v Are Orthogonal, Parallel, or Neither

Multiple Choice