92
QuizMultiple Choice

N/A — Exam

Question 92 • Algebra II

Which pair of complex numbers has a real-number product?

Answer
A
open paren 1 plus 3 i close paren times open paren 2 minus 3 i close paren
B
open paren 1 plus 3 i close paren times open paren 1 minus 3 i close paren
C
open paren 1 plus 3 i close paren times 6 i
D
open paren 1 plus 3 i close paren times 3 i

Explanation

A complex number multiplied by its conjugate gives a real number: (a + bi)(a − bi) = a² + b². In choice B, (1 + 3i)(1 − 3i) = 1² + 3² = 10, which is real. The other products have nonzero imaginary parts.

AI-written and checked against the verified answer.

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