document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583183>Question 583183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have to simplify   2+i/ 1-3i   and im lost  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372373 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "To simplify this expression you must get the imaginary unit out of the denominator.  In order to do this, use the fact that the product of two conjugates is the difference of two squares.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2\ +\ i}{1\ -\ 3i}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{2\ +\ i}{1\ -\ 3i}\right)\left(\frac{1\ +\ 3i}{1\ +\ 3i}\right)\">\r<BR>\n" );
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document.write( "which is allowed because anything divided by itself is equal to 1 and anything multiplied by 1 is equal to that same anything.\r<BR>\n" );
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document.write( "Use FOIL on the numerators and the difference of two squares rule on the denominators (remembering that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE i^2\ =\ -1\">)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{2\ +\ i}{1\ -\ 3i}\right)\left(\frac{1\ +\ 3i}{1\ +\ 3i}\right)\ =\ \frac{2\ +\ 6i\ +\ i\ -\ 3}{1\ -\ (-9)}\ =\ \frac{-1\ +\ 7i}{10}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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