Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

In complex structure, what is the equivalence if \( z = (\cos \theta + i \sin \theta) \)?
Options
A \( (\cos \theta)^k + (i \sin \theta)^k \)
B \( k(\cos (\theta + k) + i \sin (\theta + k)) \)
C \( \cos (\theta + k) + i \sin (\theta + k) \)
D \( (\cos k\theta + i \sin k\theta) \)
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

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

Hint

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

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 558 of 696
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