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

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 $- 2 \mathrm { i }$

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

---

Definitions:

WHMIS

The Workplace Hazardous Materials Information System, a Canadian system for providing information on the safe use of hazardous materials used in workplaces.

Steel-Toe

A safety feature in boots and shoes where a steel cap is inserted in the toe box, protecting the foot from falling objects or compression.

Leather Work Boots

Durable footwear made from leather, designed to provide protection and support for the feet in various work environments.

Asbestos Dust

Fine particles generated from asbestos materials, known for their hazardous health implications when inhaled.