document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040428>Question 1040428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, I'm confused on the following problem and could use some help please:\r<BR>\n" );
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document.write( "I need to multiply and simplify  (5 + 7i)^2. Am I going to multiply 5 x 5 then 7i x 7i?\r<BR>\n" );
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document.write( "I would really appreciate some help, thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655232 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're on the right track. You're missing 2 pieces though\r<BR>\n" );
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document.write( "(5 + 7i)^2 is the same as (5 + 7i)*(5 + 7i)\r<BR>\n" );
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document.write( "It's like saying x^2 is the same as x*x\r<BR>\n" );
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document.write( "Let's use FOIL to expand out (5 + 7i)*(5 + 7i)\r<BR>\n" );
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document.write( "First terms: 5*5 = 25<BR>\n" );
document.write( "Inner terms: 7i*5 = 35i<BR>\n" );
document.write( "Outer terms: 5*7i = 35i<BR>\n" );
document.write( "Last terms: 7i*7i = 49i^2\r<BR>\n" );
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document.write( "So we now add up all the terms to get \r<BR>\n" );
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document.write( "25+35i+35i+49i^2\r<BR>\n" );
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document.write( "25+70i+49i^2 ... combine like terms\r<BR>\n" );
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document.write( "25+70i+49(-1) ... replace i^2 with -1. See note\r<BR>\n" );
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document.write( "25+70i-49\r<BR>\n" );
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document.write( "-24+70i ... combine like terms\r<BR>\n" );
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document.write( "Note: since we have defined i = sqrt(-1), squaring both sides leads to i^2 = -1\r<BR>\n" );
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document.write( "The final answer is -24+70i </SPAN>\n" );
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