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

question 226

Multiple Choice

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
- $\left( 4 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right) ^ { 5 }$

• A) 1024
• B) \(1024 \mathrm { i }\)
• C) \(20 \mathrm { i }\)
• D) 0

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Definitions:

Path-Goal Theory

A theory of leadership that focuses on how leaders can motivate subordinates to achieve their goals and improve their own performance by selecting specific behaviors tailored to their needs.

Counter Behaviors

Actions taken to oppose or counteract specific behaviors or trends.

Subordinates' Environment

The workplace conditions and culture experienced by employees, which can significantly influence their morale, productivity, and satisfaction.

Evidence-Based Leadership

A leadership approach that involves making decisions and implementing strategies based on the best available evidence from various sources.