document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184324>Question 184324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify<BR>\n" );
document.write( "1/2-i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138359 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=138359\">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( "You really need to use parentheses so that it is clear what you mean.  Here, you might mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{2} - i\">\r<BR>\n" );
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document.write( "In which case, this is already simplified as much as possible.\r<BR>\n" );
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document.write( "On the other hand if you meant, as I suspect:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{2 - i}\">\r<BR>\n" );
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document.write( "Then you really should have rendered your problem thus: 1/(2 - i).\r<BR>\n" );
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document.write( "Having said all that,\r<BR>\n" );
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document.write( "First determine the conjugate of the denominator.  The conjugate of any binomial is the same binomial with the sign in the middle changed.  Hence, the conjugate of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a + b\">, for example, is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a - b\">.  In this problem the conjugate of your denominator is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ 2 + i\">\r<BR>\n" );
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document.write( "Multiply your original fraction by 1 in the form of the conjugate of the denominator divided by itself:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \left(\frac{1}{2 - i}\right)\left(\frac{2 + i}{2 + i}\right)\">\r<BR>\n" );
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document.write( "Using the difference of two squares factorization, this becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \frac{2 + i}{2^2 - i^2} = \frac{2+i}{4-(-1)}=\frac{2+i}{5}\">\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" );
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