Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Given \( z_1 = (\cos 25^\circ + i \sin 25^\circ) \) and \( z_2 = (\cos 120^\circ + i \sin 120^\circ) \), find \( z_1 z_2 \).
Options
A \( \frac{1}{2} (\cos 30^\circ + i \sin 30^\circ) \)
B \( 2 (\cos 145^\circ + i \sin 145^\circ) \)
C \( (\cos 145^\circ - i \sin 145^\circ) \)
D \( (\cos 145^\circ + i \sin 145^\circ) \)
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

Product of complex numbers in polar form: multiply moduli and add arguments. Moduli are both 1, so product modulus = 1. Arguments: 25° + 120° = 145°. So z₁z₂ = cos145° + i sin145°.

Hint

For multiplication: |z₁z₂| = |z₁||z₂|, arg(z₁z₂) = arg(z₁) + arg(z₂).

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 564 of 696
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