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

question 48

Multiple Choice

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

• A) \[\begin{array} { l }
• w _ { 1 } = \cos \left( 20 ^ { \circ } \right) + i \sin \left( 20 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 110 ^ { \circ } \right) + i \sin \left( 110 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 200 ^ { \circ } \right) + i \sin \left( 200 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 290 ^ { \circ } \right) + i \sin \left( 290 ^ { \circ } \right)
• \end{array}\]
• B) \[\begin{array} { l }
• w _ { 1 } = \cos \left( 30 ^ { \circ } \right) + i \sin \left( 30 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 120 ^ { \circ } \right) + i \sin \left( 120 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 300 ^ { \circ } \right) + i \sin \left( 300 ^ { \circ } \right)
• \end{array}\]
• C) \[\begin{array} { l }
• w _ { 1 } = \cos \left( 35 ^ { \circ } \right) + i \sin \left( 35 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 125 ^ { \circ } \right) + i \sin \left( 125 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 215 ^ { \circ } \right) + i \sin \left( 215 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 305 ^ { \circ } \right) + i \sin \left( 305 ^ { \circ } \right)
• \end{array}\]
• D) \[\begin{array} { l }
• w _ { 1 } = \cos \left( 25 ^ { \circ } \right) + i \sin \left( 25 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 115 ^ { \circ } \right) + i \sin \left( 115 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 205 ^ { \circ } \right) + i \sin \left( 205 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 295 ^ { \circ } \right) + i \sin \left( 295 ^ { \circ } \right)
• \end{array}\]
• E) \[\begin{array} { l }
• w _ { 1 } = \cos \left( 40 ^ { \circ } \right) + i \sin \left( 40 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 130 ^ { \circ } \right) + i \sin \left( 130 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 220 ^ { \circ } \right) + i \sin \left( 220 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 310 ^ { \circ } \right) + i \sin \left( 310 ^ { \circ } \right)
• \end{array}\]

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