Find All the Complex Roots $- 16$ A) B) C) D)

question 222

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) \(2 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , 2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , 2 \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , 16 \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)\)
• B) \(\sqrt [ 4 ] { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , \sqrt [ 4 ] { 2 } \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)\)
• C) \(2 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) , 2 \left( \cos 180 ^ { \circ } + i \sin 180 ^ { \circ } \right) , 2 \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right) , 2 \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)\)
• D) \(16 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , 16 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) , 16 \left( \cos 225 ^ { \circ } + i \sin 225 ^ { \circ } \right) , 16 \left( \cos 315 ^ { \circ } + i \sin 315 ^ { \circ } \right)\)

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