Find the Indicated Roots $243 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right)$

question 286

Multiple Choice

Find the indicated roots. Write the answer in polar form.
-Fifth roots of $243 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right)$

• A) \(3 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) , 3 \left( \cos 290 ^ { \circ } + i \sin 290 ^ { \circ } \right) , 3 \left( \cos 380 ^ { \circ } + i \sin 380 ^ { \circ } \right) , 3 \left( \cos 470 ^ { \circ } + i \sin 470 ^ { \circ } \right)\), \(3 \left( \cos 515 ^ { \circ } + i \sin 515 ^ { \circ } \right)\)
• B) \(3 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) , 3 \left( \cos 272 ^ { \circ } + i \sin 272 ^ { \circ } \right) , 3 \left( \cos 344 ^ { \circ } + i \sin 344 ^ { \circ } \right) , 3 \left( \cos 416 ^ { \circ } + i \sin 416 ^ { \circ } \right)\), \(3 \left( \cos 488 ^ { \circ } + i \sin 488 ^ { \circ } \right)\)
• C) \(3 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) , 3 \left( \cos 130 ^ { \circ } + i \sin 130 ^ { \circ } \right) , 3 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) , 3 \left( \cos 310 ^ { \circ } + i \sin 310 ^ { \circ } \right)\), \(3 \left( \cos 355 ^ { \circ } + i \sin 355 ^ { \circ } \right)\)
• D) \(3 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) , 3 \left( \cos 112 ^ { \circ } + i \sin 112 ^ { \circ } \right) , 3 \left( \cos 184 ^ { \circ } + i \sin 184 ^ { \circ } \right) , 3 \left( \cos 256 ^ { \circ } + i \sin 256 ^ { \circ } \right)\), \(3 \left( \cos 328 ^ { \circ } + i \sin 328 ^ { \circ } \right)\)

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Definitions:

Internal Organ

Any organ located inside the body's cavities, such as the heart, lungs, liver, or kidneys, performing essential functions.

Truss

A framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.

Protruding Mass

A lump or bulge that visibly extends out from the surface of the body or any of its structures.