SOLUTION: For what real number k does the product (25 + ki)(3+2i) equal a real number?

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Question 1077327: For what real number k does the product (25 + ki)(3+2i) equal a real number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
To cancel out the terms that end up having
an +i+ in them, I must have:
+%282i%29%2A25+=+-3k%2Ai+
+50i+=+-3k%2Ai+
+k+=+-50%2F3+
-----------------
check:
+%28+25+%2B+k%2Ai+%29%2A%28+3+%2B+2%2Ai+%29+
+%28+25+-+%2850%2F3%29%2Ai+%29%2A%28+3+%2B+2%2Ai+%29+
+75+-+50i+%2B+50i+-+%28+100%2F3+%29%2A%28-1%29+
+75+%2B+100%2F3+
+325%2F3+ ans