Use the Binomial Theorem to Expand the Following Complex Number $\left( - \frac { 3 } { 7 } - \frac { \sqrt { 7 } } { 7 } i \right) ^ { 3 }$

question 17

Multiple Choice

Use the Binomial Theorem to expand the following complex number. Write your answer in standard form.
$\left( - \frac { 3 } { 7 } - \frac { \sqrt { 7 } } { 7 } i \right) ^ { 3 }$

• A) \(\frac { 36 } { 343 } - \frac { 20 \sqrt { 7 } } { 343 } i\)
• B) \(\frac { 36 } { 343 } + \frac { 20 \sqrt { 7 } } { 49 } i\)
• C) \(- \frac { 36 } { 49 } - \frac { 20 \sqrt { 7 } } { 343 } i\)
• D) \(- \frac { 27 } { 343 } + \frac { \sqrt { 7 } } { 49 } i\)
• E) \(- \frac { 27 } { 343 } - \frac { \sqrt { 7 } } { 49 } i\)

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Definitions:

Major Organic

This term lacks specificity without additional context but could refer to the principal or most significant organic compound(s) or molecule(s) in a given context.

Methyl Ester

Organic compounds formed from the reaction of an acid with methanol, characterized by a methyl group attached to the ester functional group.

Carboxylic Acid

Organic acids characterized by the presence of at least one carboxyl group (-COOH), which gives them their acidic properties.

Hell-Volhard-Zelinsky

A chemical reaction that halogenates carboxylic acids at the alpha carbon with a bromine or chlorine in the presence of phosphorus.