Find All Cube Roots of the Complex Number $64 \operatorname { cis } 120 ^ { \circ }$

question 198

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $64 \operatorname { cis } 120 ^ { \circ }$

• A) \(4 \left( - \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) , 4 \left( \frac { 1 } { 2 } \mathrm { i } - \frac { \sqrt { 3 } } { 2 } \right) , 4 \left( \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right)\)
• B) \(4 ( .6428 + .7660 \mathrm { i } ) , 4 ( - .3420 + .9397 \mathrm { i } ) , 4 ( .9848 - .1736 \mathrm { i } )\)
• C) \(4 \left( \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( - \frac { \sqrt { 3 } } { 2 } + \frac { 1 } { 2 } \mathrm { i } \right) , 4 \left( \frac { \sqrt { 3 } } { 2 } - \frac { 1 } { 2 } \mathrm { i } \right)\)
• D) \(4 ( .7660 + .6428 \mathrm { i } ) , 4 ( - .9397 + .3420 \mathrm { i } ) , 4 ( .1736 - .9848 \mathrm { i } )\)

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