Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Polar form of \( 4 + 4\sqrt{3}i \) is
Options
A \( 4\cos\frac{\pi}{3} + i\sin\frac{\pi}{3} \)
B \( 4\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3} \)
C \( 8\cos\frac{\pi}{3} + i\sin\frac{\pi}{3} \)
Correct Answer
D \( 8\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3} \)
Correct Answer

Option C is the correct answer.

Detailed Explanation

Modulus = √(4² + (4√3)²) = √(16+48)=√64=8. Argument = tan⁻¹(4√3/4)=tan⁻¹(√3)=π/3. So polar form is 8(cos π/3 + i sin π/3).

Hint

Find r = √(a²+b²) and θ = tan⁻¹(b/a).

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 565 of 696
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