document.write( "Question 207549: Expand: (2+3i)^2 \n" ); document.write( "

Algebra.Com's Answer #156940 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"%282%2B3i%29%2A%282%2B3i%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"%282%2B3i%29%5E2\"$ Expand\r
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\n" ); document.write( "\n" ); document.write( " $\"%282%29%282%29%2B%282%29%283i%29%2B%283i%29%282%29%2B%283i%29%283i%29\"$ FOIL.\r
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\n" ); document.write( "\n" ); document.write( " $\"4%2B6i%2B6i%2B9i%5E2\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"4%2B6i%2B6i%2B9%28-1%29\"$ Replace $\"i%5E2\"$ with $\"-1\"$ . Note: $\"i%5E2=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"4%2B6i%2B6i-9\"$ Multiply.\r
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\n" ); document.write( "\n" ); document.write( " $\"-5%2B12i\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So $\"%282%2B3i%29%5E2=-5%2B12i\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So the expression is now in standard form $\"a%2Bbi\"$ where $\"a=-5\"$ and $\"b=12\"$ \r
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