Question Detail
Question
Simplify: \(\frac{(2+i)(3+2i)}{4+i}\)
Correct Answer
Option C is the correct answer.
Detailed Explanation
First multiply numerator: (2+i)(3+2i) = 6+4i+3i+2i² = 6+7i-2 = 4+7i. Then divide by (4+i): (4+7i)/(4+i) × (4-i)/(4-i) = (16 -4i +28i -7i²)/(16+1) = (16+24i+7)/17 = (23+24i)/17 = 23/17 + (24/17)i. That matches option B. Option C is 23/17 + 3/17i, which is different. So B is correct.
Hint
Multiply numerator and denominator by the conjugate of the denominator.