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

question 152

Multiple Choice

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

• A) \(\sqrt [ 3 ] { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 310 ^ { \circ }\)
• B) \(\sqrt { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 310 ^ { \circ }\)
• C) \(\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 290 ^ { \circ }\)
• D) \(\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 270 ^ { \circ }\)

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