Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

If (3a - 2b) + i(2a - b) = 10 + 2i, find a and b.
Options
A a = 2, b = -3
B a = -2, b = -3
C a = -6, b = -14
D a = 6, b = -14
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

Real parts: 3a - 2b = 10; Imaginary: 2a - b = 2. Solve: from second, b = 2a - 2. Substitute: 3a - 2(2a-2) = 10 ⇒ 3a - 4a + 4 = 10 ⇒ -a = 6 ⇒ a = -6, then b = 2(-6)-2 = -12-2 = -14. So a = -6, b = -14. That matches option C. Option D is a=6,b=-14. C is correct.

Hint

Equate real and imaginary parts separately, then solve the system.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 622 of 696
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