15
AssignmentMultiple Choice

Performing Operations with Complex Numbers

Question 15 • Algebra III A

Which pair of complex factors results in a real-number product?

Answer
A
15(–15i)
B
3i(1 – 3i)
C
(8 + 20i)(–8 – 20i)
D
(4 + 7i)(4 – 7i)

Explanation

A complex number multiplied by its conjugate gives a real number: (a + bi)(a − bi) = a² + b². Choice D has conjugate factors, so (4 + 7i)(4 − 7i) = 4² + 7² = 65, which is real. The other products have nonzero imaginary parts.

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