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Find All the Complex Roots 3+i\sqrt { 3 } + i

Question 265

Multiple Choice

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fifth roots of 3+i\sqrt { 3 } + i


A) 25(cos⁡30∘+isin⁡30∘) ,25(cos⁡102∘+isin⁡102∘) ,25(cos⁡174∘+isin⁡174∘) ,25(cos⁡246∘+isin⁡246∘) \sqrt [ 5 ] { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 102 ^ { \circ } + i \sin 102 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 174 ^ { \circ } + i \sin 174 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 246 ^ { \circ } + i \sin 246 ^ { \circ } \right) , 25(cos⁡318∘+isin⁡318∘) \sqrt [ 5 ] { 2 } \left( \cos 318 ^ { \circ } + i \sin 318 ^ { \circ } \right)
B) 32(cos⁡6∘+isin⁡6∘) ,32(cos⁡78∘+isin⁡78∘) ,32(cos⁡150∘+isin⁡150∘) ,32(cos⁡222∘+isin⁡222∘) 32 \left( \cos 6 ^ { \circ } + i \sin 6 ^ { \circ } \right) , 32 \left( \cos 78 ^ { \circ } + i \sin 78 ^ { \circ } \right) , 32 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) , 32 \left( \cos 222 ^ { \circ } + i \sin 222 ^ { \circ } \right) , 32(cos⁡294∘+isin⁡294∘) 32 \left( \cos 294 ^ { \circ } + i \sin 294 ^ { \circ } \right)
C) 32(cos⁡30∘+isin⁡30∘) ,32(cos⁡102∘+isin⁡102∘) ,32(cos⁡174∘+isin⁡174∘) ,32(cos⁡246∘+isin⁡246∘) 32 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) , 32 \left( \cos 102 ^ { \circ } + i \sin 102 ^ { \circ } \right) , 32 \left( \cos 174 ^ { \circ } + i \sin 174 ^ { \circ } \right) , 32 \left( \cos 246 ^ { \circ } + i \sin 246 ^ { \circ } \right) , 32(cos⁡318∘+isin⁡318∘) 32 \left( \cos 318 ^ { \circ } + i \sin 318 ^ { \circ } \right)

D) 25(cos⁡6∘+isin⁡6∘) ,25(cos⁡78∘+isin⁡78∘) ,25(cos⁡150∘+isin⁡150∘) ,25(cos⁡222∘+isin⁡222∘) \sqrt [ 5 ] { 2 } \left( \cos 6 ^ { \circ } + i \sin 6 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 78 ^ { \circ } + i \sin 78 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 222 ^ { \circ } + i \sin 222 ^ { \circ } \right) , 25(cos⁡294∘+isin⁡294∘) \sqrt [ 5 ] { 2 } \left( \cos 294 ^ { \circ } + i \sin 294 ^ { \circ } \right)

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