Find All Cube Roots of the Complex Number $$- 6 \sqrt { 3 } - 6 i$$

question 368

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $$- 6 \sqrt { 3 } - 6 i$$

• A) \(\sqrt { 6 } \operatorname { cis } 70 ^ { \circ } , \sqrt { 6 } \operatorname { cis } 190 ^ { \circ } , \sqrt { 6 } \operatorname { cis } 310 ^ { \circ }\)
• B) \(\sqrt [ 3 ] { 12 } \operatorname { cis } 70 ^ { \circ } , \sqrt [ 3 ] { 12 } \operatorname { cis } 190 ^ { \circ } , \sqrt [ 3 ] { 12 } \operatorname { cis } 310 ^ { \circ }\)
• C) \(\sqrt [ 3 ] { 6 } \operatorname { cis } 70 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 190 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 310 ^ { \circ }\)
• D) \(\sqrt [ 3 ] { 12 } \operatorname { cis } 80 ^ { \circ } , \sqrt [ 3 ] { 6 }\) cis \(200 ^ { \circ } , \sqrt [ 3 ] { 12 }\) cis \(320 ^ { \circ }\)

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