document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275548>Question 275548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is my last Algebra 2 problem and I have no idea how to solve this.  The problem is to simplify -1/(3+i)  using imaginary numbers.  To me it appears that this is as simplified as it can get.\r<BR>\n" );
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document.write( "Thank you.<BR>\n" );
document.write( "Mark </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200951 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=200951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> simplify -1/(3+i) using imaginary numbers<BR>\n" );
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document.write( "\"Simplified\" in this case means \"no imaginary numbers in the denominator\".<BR>\n" );
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document.write( "So, multiply numerator and denominator by the conjugate of 3+i, which is 3-i.<BR>\n" );
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document.write( "You get:<BR>\n" );
document.write( "[-1(3-i)]/[(3+i)(3-i)]<BR>\n" );
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document.write( "The form in the denominator is (a+b)(a-b)<BR>\n" );
document.write( "That product is always a^2 - b^2<BR>\n" );
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document.write( "So for your problem you get:<BR>\n" );
document.write( "[(-3+i)]/[3^2-(i)^2]<BR>\n" );
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document.write( "= (-3+i)/(9 + 1)<BR>\n" );
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document.write( "= (-3+i)/10<BR>\n" );
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document.write( "That is the simplified form.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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