document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120434>Question 120434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI! May I get some help with this expression?\r<BR>\n" );
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document.write( "Evaluate the expression and write the result in the form a + bi.\r<BR>\n" );
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document.write( "(6 + 5i)^-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88269 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=88269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+%2B+5i%29%5E-1 ALIGN=MIDDLE  ALT=\"%286+%2B+5i%29%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%286+%2B+5i%29 ALIGN=MIDDLE  ALT=\"1%2F%286+%2B+5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the expression as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%286+%2B+5i%29 ALIGN=MIDDLE  ALT=\"1%2F%286+%2B+5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E-2=1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x%5E-2=1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{1}{6+5i}\right)\left(\frac{6-5i}{6-5i}\right)\"> Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{6-5i}{6-5i}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{6-5i}{61}\"> Foil and Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{6}{61}-\frac{5}{61}i\"> Break up the fraction. So it is now in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bbi ALIGN=MIDDLE  ALT=\"a%2Bbi\"   DISABLED_style= \"max-width:90%; height:auto;\" > form where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6%2F61 ALIGN=MIDDLE  ALT=\"a=6%2F61\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5%2F61 ALIGN=MIDDLE  ALT=\"b=-5%2F61\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(6+5i\right)^{-1}\"> simplifies to  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{6}{61}-\frac{5}{61}i\"> \r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(6+5i\right)^{-1}=\frac{6}{61}-\frac{5}{61}i\"> <BR>\n" );
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