Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

If \(z = 4(\cos 110^\circ + i \sin 110^\circ)\), find \(z^3\).
Options
A \(16(\cos 330^\circ + i \sin 330^\circ)\)
B \(4(\cos 330^\circ + i \sin 330^\circ)\)
C \(64(\cos 330^\circ - i \sin 330^\circ)\)
D \(64(\cos 330^\circ + i \sin 330^\circ)\)
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

By De Moivre's Theorem: z³ = 4³ (cos(3×110°) + i sin(3×110°)) = 64(cos330° + i sin330°).

Hint

Apply (r(cosθ + i sinθ))ⁿ = rⁿ(cos(nθ) + i sin(nθ)).

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 594 of 696
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