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Find All the Complex Roots B) C) D)

Question 187

Multiple Choice

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fourth roots of -16 A) 2(cos⁡45∘+isin⁡45∘) ,2(cos⁡135∘+isin⁡135∘) ,2(cos⁡225∘+isin⁡225∘) ,16(cos⁡315∘+isin⁡315∘) 2 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , 2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , 2 \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , 16 \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)
B) 24(cos⁡45∘+isin⁡45∘) ,24(cos⁡135∘+isin⁡135∘) ,24(cos⁡225∘+isin⁡225∘) ,24(cos⁡315∘+isin⁡315∘) \sqrt [ 4 ] { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)
C) 2(cos⁡90∘+isin⁡90∘) ,2(cos⁡180∘+isin⁡180∘) ,2(cos⁡270∘+isin⁡270∘) ,2(cos⁡360∘+isin⁡360∘) 2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) , 2 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right) , 2 \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right) , 2 \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)
D) 16(cos⁡45∘+isin⁡45∘) ,16(cos⁡135∘+isin⁡135∘) ,16(cos⁡225∘+isin⁡225∘) ,16(cos⁡315∘+isin⁡315∘) 16 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , 16 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , 16 \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , 16 \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)

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