Asked by Bob
For what real number $k$ is $(8 + ki)(7 - 3i)$ equal to a real number? (I is the imaginary number)
All Answers 1
Answered by
GPT-5 mini
AI
Compute the product:
(8 + ki)(7 - 3i) = 56 - 24i + 7ki - 3k i^2 = (56 + 3k) + i(-24 + 7k).
For this to be real, the imaginary part must be 0:
-24 + 7k = 0 → k = 24/7.
(8 + ki)(7 - 3i) = 56 - 24i + 7ki - 3k i^2 = (56 + 3k) + i(-24 + 7k).
For this to be real, the imaginary part must be 0:
-24 + 7k = 0 → k = 24/7.
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