document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193093>Question 1193093</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply. Simplify Completely \r<BR>\n" );
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document.write( "(sqrt(-2) - sqrt(-27)) * (sqrt(-2) + sqrt (-75)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825068 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (sqrt(-2) - sqrt(-27)) * (sqrt(-2) + sqrt (-75)) is equal to:<BR>\n" );
document.write( "sqrt(-2) * (sqrt(-2) + sqrt (-75)) - sqrt(-27) * (sqrt(-2) + sqrt(-75)) which is equal to:<BR>\n" );
document.write( "sqrt(-2) * sqrt(-2) + sqrt(-2) * sqrt(-75) - sqrt(-27) * sqrt(-2) - sqrt(-27) * sqrt(-75).\r<BR>\n" );
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document.write( "note that:\r<BR>\n" );
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document.write( "sqrt(-2) = sqrt(2) * i<BR>\n" );
document.write( "sqrt(-75) = sqrt(75) * i<BR>\n" );
document.write( "sqrt(-27) = sqrt(27) * i\r<BR>\n" );
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document.write( "consequently:\r<BR>\n" );
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document.write( "sqrt(-2) * sqrt(-2) + sqrt(-2) * sqrt(-75) - sqrt(-27) * sqrt(-2) - sqrt(-27) * sqrt(-75) becomes:<BR>\n" );
document.write( "sqrt(2)*i * sqrt(2)*i + sqrt(2)*i * sqrt(75)*i - sqrt(27)*i * sqrt(2)*i - sqrt(27)*i * sqrt75)*i which becomes:<BR>\n" );
document.write( "sqrt(2)*sqrt(2)*i^2 + sqrt(2)*sqrt(75)*i^2 - sqrt(27)*sqrt(2)*i^2 - sqrt(27)*sqrt(75)*i^2 which becomes:<BR>\n" );
document.write( "sqrt(4)*i^2 + sqrt(150)*i^2 - sqrt(54)*i^2 - sqrt(2025)*i^2.\r<BR>\n" );
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document.write( "since i^2 = -1, then:\r<BR>\n" );
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document.write( "sqrt(4)*i^2 + sqrt(150)*i^2 - sqrt(54)*i^2 - sqrt(2025)*i^2 becomes:<BR>\n" );
document.write( "sqrt(4)*-1 + sqrt(150)*-1 - sqrt(54)*-1 - sqrt(2025)*-1 which becomes:<BR>\n" );
document.write( "-sqrt(4) - sqrt(150) + sqrt(54) + sqrt(2025) which is equal to 38.10102051.\r<BR>\n" );
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document.write( "your solution should be 38.10102051.\r<BR>\n" );
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document.write( "note that the rules of the value of i in complex arithmetic equations is:\r<BR>\n" );
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document.write( "i^1 = i<BR>\n" );
document.write( "i^2 = -1<BR>\n" );
document.write( "i^3 = -i<BR>\n" );
document.write( "i^4 = 1\r<BR>\n" );
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document.write( "this is a repetitive pattern that repeats for every set of 4.\r<BR>\n" );
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document.write( "to determine how to analyze this for i ^ something greater than 4, an example should show you how it's done.\r<BR>\n" );
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document.write( "i^38 is the example.<BR>\n" );
document.write( "divide 38 by 4 to get 9.5<BR>\n" );
document.write( "9 * 4 = 36<BR>\n" );
document.write( "38 minus 36 = 2<BR>\n" );
document.write( "i^2 = -1<BR>\n" );
document.write( "therefore i^38 = -1<BR>\n" );
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