Find All Cube Roots of the Complex Number $$2 + 2 i \sqrt { 3 }$$

question 30

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $$2 + 2 i \sqrt { 3 }$$

• A) \(\sqrt [ 3 ] { 4 } \operatorname { cis } 30 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 150 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 270 ^ { \circ }\)
• B) \(\sqrt [ 3 ] { 4 } \operatorname { cis } 20 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 140 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 260 ^ { \circ }\)
• C) \(\sqrt { 2 } \operatorname { cis } 20 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 140 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 260 ^ { \circ }\)
• D) \(\sqrt { 4 } \operatorname { cis } 20 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 140 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 260 ^ { \circ }\)