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MTH 101 MTH 101 Past Questions Objective Question

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Polar form of \(z = 4 + 4\sqrt{3}i\) is

A \(8(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3})\)

Correct Answer

B \(4(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3})\)

C \(8(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3})\)

D \(4(\cos\frac{\pi}{3} + i\sin\frac{\pi}{3})\)

Option A is the correct answer.

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).

Find r = √(a²+b²) and θ = tan⁻¹(b/a).

Course: MTH 101

Topic: MTH 101 Past Questions

Type: Objective

Difficulty: Not specified

Question 653 of 696

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