document.write( "Question 529806: Simplify 5
\n" ); document.write( " ______
\n" ); document.write( " 2 + 4i . \n" ); document.write( "

Algebra.Com's Answer #349741 by swincher4391(1107) $\"\"$ $\"About$

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What you want to do is multiply by conjugate/conjugate of your complex number (2+4i). The conjugate of (2+4i) is (2-4i). What will happen is really nice. Your denominator will become a real number due to the fact that you are going to get a difference of two squares, and since i^2 = -1, you'll just end up with a real number. Watch and see.\r
\n" ); document.write( "\n" ); document.write( "(5/(2+4i)) * (2-4i)/(2-4i)\r
\n" ); document.write( "\n" ); document.write( "The numerator: 5*(2-4i) = 10 - 20i \r
\n" ); document.write( "\n" ); document.write( "The denominator: (2+4i)(2-4i)\r
\n" ); document.write( "\n" ); document.write( "Foil.\r
\n" ); document.write( "\n" ); document.write( "=4 - 8i + 8i -16i^2
\n" ); document.write( "=4 + 16 = 20 A REAL NUMBER!\r
\n" ); document.write( "\n" ); document.write( "So we have (10-20i)/20\r
\n" ); document.write( "\n" ); document.write( "Factor out a 10 out of the numerator.\r
\n" ); document.write( "\n" ); document.write( "(10(1-2i))/20
\n" ); document.write( "Divide through by 10 to get:\r
\n" ); document.write( "\n" ); document.write( "(1-2i)/2 <----- Answer \n" ); document.write( "

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