Use DeMoivre's Theorem to Find the Indicated Power of the Following

question 116

Multiple Choice

Use DeMoivre's Theorem to find the indicated power of the following complex number. $\left[ - 2 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right) \right] ^ { 6 }$

• A)-4
• B)-8
• C) \(64 + 64 \sqrt { 3 }\)
• D) \(32 + 32 \sqrt { 3 }\)
• E)8

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Definitions:

Fixed Number

A value that remains constant and does not change in different situations or equations.

Independent Trials

Refer to experiments or trials in which the outcome of any single trial does not affect the outcomes of any other trials.

Null Hypothesis

A statistically formulated assertion that posits no relationship or difference between two or more groups or factors, serving as a default position until evidence suggests otherwise.

Chi-Square Test Statistic

A value derived from the chi-square test, representing the sum of the squared differences between observed and expected frequencies divided by the expected frequencies.