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Find All Cube Roots of the Complex Number 33+3i- 3 \sqrt { 3 } + 3 i

Question 152

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- 33+3i- 3 \sqrt { 3 } + 3 i


A) 33cis70,33cis190,33cis310\sqrt [ 3 ] { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt [ 3 ] { 3 } \operatorname { cis } 310 ^ { \circ }
B) 3cis70,3cis190,3cis310\sqrt { 3 } \operatorname { cis } 70 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 190 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 310 ^ { \circ }
C) 63cis50,63cis170,63cis290\sqrt [ 3 ] { 6 } \operatorname { cis } 50 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 170 ^ { \circ } , \sqrt [ 3 ] { 6 } \operatorname { cis } 290 ^ { \circ }
D) 63cis50,63cis170,63cis270\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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