Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

\( (\cos \theta + i \sin \theta)^n \) is equal to
Options
A \( \cos n\theta + i \sin n\theta \)
Correct Answer
B \( \sin n\theta + i \cos n\theta \)
C \( \cos n\theta - i \sin n\theta \)
D \( \cos(-\theta) + i \sin(-\theta) \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

By De Moivre's Theorem, (cosθ + i sinθ)^n = cos(nθ) + i sin(nθ).

Hint

De Moivre's Theorem is the standard result.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 567 of 696
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