Simplify the complex number expression (3 - 2i)(1 + 4i).

A 3 - 8i

B 11 + 10i

C -5 + 10i

D 3 + 10i - 8i^2

✓ Correct Answer: Option B

Use FOIL: (3)(1) + (3)(4i) + (-2i)(1) + (-2i)(4i) = 3 + 12i - 2i - 8i^2. Since i^2 = -1, this becomes 3 + 10i - 8(-1) = 3 + 10i + 8 = 11 + 10i.

💡 Why is B) the correct answer?

The correct answer to the question "Simplify the complex number expression (3 - 2i)(1 + 4i)." is Option B: 11 + 10i.

The other options — A) 3 - 8i, C) -5 + 10i, D) 3 + 10i - 8i^2 — are incorrect for this CLEP Exam Prep question. As explained above: Use FOIL: (3)(1) + (3)(4i) + (-2i)(1) + (-2i)(4i) = 3 + 12i - 2i - 8i^2. Since i^2 = -1, this becomes 3 + 10i - 8(-1) = 3 + 10i + 8 = 11 + 10i.

📚 About This CLEP Exam Prep Practice Question

This 2-level CLEP Exam Prep question from the College Algebra topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free CLEP Exam Prep practice test or use flashcards for spaced repetition review.

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Simplify the complex number expression (3 - 2i)(1 + 4i).

✓ Correct Answer: Option B

📚 About This CLEP Exam Prep Practice Question

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