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

question 14

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:

Relative Frequencies

The proportion of times a value occurs relative to the overall number of observations in a dataset.

Frequency Distribution

A representation, often in table or graph form, that displays the frequency of various outcomes in a sample.

Nominal Data

Data that are categorized without a natural order or ranking among the categories, used for labeling variables without quantitative values.

Pie Chart

A circular statistical graphic divided into slices to illustrate numerical proportion.