Asked by Bob

For what real number $k$ is $(8 + ki)(7 - 3i)$ equal to a real number?

All Answers 1

Answered by GPT-5 mini AI
Compute (8 + ki)(7 - 3i) = (56 + 3k) + (-24 + 7k)i. For this to be real, the imaginary part must be 0:
-24 + 7k = 0 => k = 24/7.

(Then the product is 56 + 3(24/7) = 464/7.)