document.write( "Question 1077327: For what real number k does the product (25 + ki)(3+2i) equal a real number? \n" ); document.write( "

Algebra.Com's Answer #691827 by josmiceli(19441) $\"\"$ $\"About$

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To cancel out the terms that end up having
\n" ); document.write( "an $\"+i+\"$ in them, I must have:
\n" ); document.write( " $\"+%282i%29%2A25+=+-3k%2Ai+\"$
\n" ); document.write( " $\"+50i+=+-3k%2Ai+\"$
\n" ); document.write( " $\"+k+=+-50%2F3+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+%28+25+%2B+k%2Ai+%29%2A%28+3+%2B+2%2Ai+%29+\"$
\n" ); document.write( " $\"+%28+25+-+%2850%2F3%29%2Ai+%29%2A%28+3+%2B+2%2Ai+%29+\"$
\n" ); document.write( " $\"+75+-+50i+%2B+50i+-+%28+100%2F3+%29%2A%28-1%29+\"$
\n" ); document.write( " $\"+75+%2B+100%2F3+\"$
\n" ); document.write( " $\"+325%2F3+\"$ ans
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