Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fifth roots of $- 2 i$
A) $32 \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , 32 \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , 32 \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , 32 \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right)$, $32 \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)$
B) $\sqrt [ 5 ] { 2 } \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right)$, $\sqrt [ 5 ] { 2 } \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)$

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

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

Question

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fifth roots of $- 2 i$
A) $32 \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , 32 \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , 32 \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , 32 \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right)$, $32 \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)$
B) $\sqrt [ 5 ] { 2 } \left( \cos 54 ^ { \circ } + i \sin 54 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 126 ^ { \circ } + i \sin 126 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 198 ^ { \circ } + i \sin 198 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right)$, $\sqrt [ 5 ] { 2 } \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)$

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

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

Quizplus · Accepted Answer

The magnitude of the roots is $\sqrt[5]{2}$ because the magnitude of $-2i$ is 2, and the roots are spaced evenly around the circle, starting from the angle of $-2i$ which is $270^\circ$, then adding $72^\circ$ (360°/5) for each subsequent root.

Find All the Complex Roots −2i- 2 i−2i A) 32(cos⁡342∘+isin⁡342∘)32 \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)32(cos342∘+isin342∘)

Find All the Complex Roots $- 2 i$ A) $32 \left( \cos 342 ^ { \circ } + i \sin 342 ^ { \circ } \right)$