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

question 21

Multiple Choice

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

• A)
• \(\begin{array} { l }
• w _ { 1 } = \cos \left( 50 ^ { \circ } \right) + i \sin \left( 50 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 140 ^ { \circ } \right) + i \sin \left( 140 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 230 ^ { \circ } \right) + i \sin \left( 230 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 320 ^ { \circ } \right) + i \sin \left( 320 ^ { \circ } \right)
• \end{array}\)
• 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)
• \(\begin{array} { l }
• w _ { 1 } = \cos \left( 70 ^ { \circ } \right) + i \sin \left( 70 ^ { \circ } \right) \\
• w _ { 2 } = \cos \left( 160 ^ { \circ } \right) + i \sin \left( 160 ^ { \circ } \right) \\
• w _ { 3 } = \cos \left( 250 ^ { \circ } \right) + i \sin \left( 250 ^ { \circ } \right) \\
• w _ { 4 } = \cos \left( 340 ^ { \circ } \right) + i \sin \left( 340 ^ { \circ } \right)
• \end{array}\)

---

Definitions:

Intelligible Word

A word that is spoken or written in a way that is easily understood.

Pragmatics

A branch of linguistics dealing with the use of language in social contexts and the ways in which people convey meaning through communication.

Formal Etiquette

The set of conventional rules for polite behavior in societal or official life, often used in ceremonies, formal events, and in interactions among dignitaries.

Syntax

The set of rules that dictate the structure and order of words in sentences for the purposes of communication in a language.