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Find All the Complex Roots −2i- 2 \mathrm { i }

Question 114

Multiple Choice

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fifth roots of −2i- 2 \mathrm { i }


A) 32(cos⁡54∘+isin⁡54∘) ,32(cos⁡126∘+isin⁡126∘) ,32(cos⁡198∘+isin⁡198∘) ,32(cos⁡270∘+isin⁡270∘) 32 \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , 32 \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , 32 \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , 32 \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right) , 32(cos⁡342∘+isin⁡342∘) 32 \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)
B) 25(cos⁡54∘+isin⁡54∘) ,25(cos⁡126∘+isin⁡126∘) ,25(cos⁡198∘+isin⁡198∘) ,25(cos⁡270∘+isin⁡270∘) \sqrt [ 5 ] { 2 } \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right) , 25(cos⁡342∘+isin⁡342∘) \sqrt [ 5 ] { 2 } \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)

C) 25(cos⁡45∘+isin⁡45∘) ,25(cos⁡117∘+isin⁡117∘) ,25(cos⁡189∘+isin⁡189∘) ,25(cos⁡261∘+isin⁡261∘) \sqrt [ 5 ] { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 117 ^ { \circ } + i \sin 117 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 189 ^ { \circ } + i \sin 189 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 261 ^ { \circ } + i \sin 261 ^ { \circ } \right) , 25(cos⁡333∘+isin⁡333∘) \sqrt [ 5 ] { 2 } \left( \cos 333 ^ { \circ } + i \sin 333 ^ { \circ } \right)

D) 24(cos⁡54∘+isin⁡54∘) ,24(cos⁡126∘+isin⁡126∘) ,24(cos⁡198∘+isin⁡198∘) ,24(cos⁡270∘+isin⁡270∘) \sqrt [ 4 ] { 2 } \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right) , 24(cos⁡342∘+isin⁡342∘) \sqrt [ 4 ] { 2 } \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)

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