Question Detail

MTH 101 MTH 101 Past Questions Objective Question
Take CBT

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 \(\cos(\frac{\pi}{2} - n\theta) + i \sin(\frac{\pi}{2} - n\theta)\)
D \(\cos n\theta - i \sin n\theta\)
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 595 of 696
Previous Course Details Next