ACT Math · Complex numbers
What is the product (3+2i)(1-4i)?
What is the product ?
Answer and explanation
Answer: D: 11 - 10i
Expand: (3)(1) + (3)(−4i) + (2i)(1) + (2i)(−4i) = 3 − 12i + 2i − 8i². Since i² = −1, −8i² = 8, giving 3 + 8 − 10i = 11 − 10i. Choice C drops the negative sign that results from combining the imaginary terms correctly. Choice B multiplies only the first and last terms, skipping the outer and inner products.
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