Find All the Complex Roots $\sqrt { 3 } + i$

question 139

Multiple Choice

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
-The complex fifth roots of $\sqrt { 3 } + i$

• A) \(\sqrt [ 5 ] { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 102 ^ { \circ } + i \sin 102 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 174 ^ { \circ } + i \sin 174 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 246 ^ { \circ } + i \sin 246 ^ { \circ } \right)\), \(\sqrt [ 5 ] { 2 } \left( \cos 318 ^ { \circ } + i \sin 318 ^ { \circ } \right)\)
• B) \(32 \left( \cos 6 ^ { \circ } + i \sin 6 ^ { \circ } \right) , 32 \left( \cos 78 ^ { \circ } + i \sin 78 ^ { \circ } \right) , 32 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) , 32 \left( \cos 222 ^ { \circ } + i \sin 222 ^ { \circ } \right)\), \(32 \left( \cos 294 ^ { \circ } + \mathrm { i } \sin 294 ^ { \circ } \right)\)
• C) \(32 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) , 32 \left( \cos 102 ^ { \circ } + i \sin 102 ^ { \circ } \right) , 32 \left( \cos 174 ^ { \circ } + i \sin 174 ^ { \circ } \right) , 32 \left( \cos 246 ^ { \circ } + i \sin 246 ^ { \circ } \right)\), \(32 \left( \cos 318 ^ { \circ } + i \sin 318 ^ { \circ } \right)\)
• D) \(\sqrt [ 5 ] { 2 } \left( \cos 6 ^ { \circ } + i \sin 6 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 78 ^ { \circ } + i \sin 78 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) , \sqrt [ 5 ] { 2 } \left( \cos 222 ^ { \circ } + i \sin 222 ^ { \circ } \right)\), \(\sqrt [ 5 ] { 2 } \left( \cos 294 ^ { \circ } + i \sin 294 ^ { \circ } \right)\)

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Definitions:

Times Interest Earned

A financial metric indicating how many times a company's operating income can cover its interest expense, used to assess financial stability.

Net Income

The total profit of a company after all expenses and taxes have been deducted from total revenues.

Interest Expense

The cost incurred by an entity for borrowed funds; interest expense is a non-operating cost shown on the income statement.

Current Ratio

A financial metric assessing a firm's capability to meet its short-term liabilities or debts due within a year.