Find the Indicated Roots $- 1 - \sqrt { 3 } i$

question 34

Multiple Choice

Find the indicated roots. Write the answer in a + bi form.
-Fourth roots of $- 1 - \sqrt { 3 } i$

• A) \(\frac { 1 } { 4 } ( 1 + \sqrt { 3 } i ) , \frac { 1 } { 4 } ( - \sqrt { 3 } + i ) , \frac { 1 } { 4 } ( - 1 - \sqrt { 3 } i ) , \frac { 1 } { 4 } ( \sqrt { 3 } - i )\)
• B) \(\frac { \sqrt [ 4 ] { 2 } } { 2 } ( 1 + \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( - \sqrt { 3 } + i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( - 1 - \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( \sqrt { 3 } - i )\)
• C) \(\frac { 1 } { 4 } \left( 1 + \sqrt { 3 } \mathrm { i } , , \frac { 1 } { 4 } ( \sqrt { 3 } + i ) , \frac { 1 } { 4 } ( 1 - \sqrt { 3 } i ) , \frac { 1 } { 4 } ( \sqrt { 3 } - i ) \right.\)
• D) \(\frac { \sqrt [ 4 ] { 2 } } { 2 } ( 1 + \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( \sqrt { 3 } + i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( 1 - \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( \sqrt { 3 } - i )\)

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Definitions:

Combustion

A chemical reaction that occurs when a substance reacts with oxygen to give off heat and light, often producing flame.

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A rephrased definition: Chemical compounds or mixtures that release a large amount of energy in a very short time through blasts or combustion.

Carbon Dioxide

A colorless, odorless gas with the formula CO2, produced by burning carbon and organic compounds and by respiration.

Organic Material

Matter obtained from living organisms, typically consisting of compounds like carbohydrates, proteins, lipids, and nucleic acids.