Use De Moivre's Theorem to Find the Indicated Power of the Complex

question 14

Multiple Choice

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
- $$\left( - \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right) 10$$

• A) \(\frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }\)
• B) \(- \frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } i\)
• C) \(\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 2 } \mathrm { i }\)
• D) \(- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } i\)

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Definitions:

Audience Effect

The impact of an audience's presence on an individual's performance, typically leading to improvement or deterioration depending on the task's complexity and the performer's expertise.

Social Facilitation

The improvement in performance witnessed when individuals are observed or are in the presence of others, due to increased arousal.

Social Groups

Collections of people who interact with each other and share similar characteristics or a sense of unity.

Evaluation Apprehension Model

The argument that the physical presence of members of the same species causes drive because people have learnt to be apprehensive about being evaluated.