Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

If \( (a - 2b) + i(2a - b) = 4 + 2i \), find \( a \) and \( b \).
Options
A \( a = 0, b = -2 \)
Correct Answer
B \( a = -2, b = -3 \)
C \( a = 0, b = -4 \)
D \( a = 2, b = -1 \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

Equate real and imaginary parts: a - 2b = 4, and 2a - b = 2. Solving: multiply the second equation by 2: 4a - 2b = 4. Subtract the first equation from this: (4a-2b) - (a-2b) = 4-4 => 3a = 0 => a=0. Then from a-2b=4 => -2b=4 => b=-2.

Hint

Set the real parts equal and the imaginary parts equal, then solve the system.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 545 of 696
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