document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189013>Question 189013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> True of false?\r<BR>\n" );
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document.write( "The number (1/2)i is the reciprocal of 2i.\r<BR>\n" );
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document.write( "Could you please provide a detailed explanation on how you achieved you answer, and show me how the product of 2i and its reciprocal equal 1.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141761 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=141761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2i ALIGN=MIDDLE  ALT=\"x=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The reciprocal of \"x\" is simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282i%29 ALIGN=MIDDLE  ALT=\"1%2F%282i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2i ALIGN=MIDDLE  ALT=\"x=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the reciprocal of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2i ALIGN=MIDDLE  ALT=\"2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282i%29 ALIGN=MIDDLE  ALT=\"1%2F%282i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29i ALIGN=MIDDLE  ALT=\"%281%2F2%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "So the statement is false.\r<BR>\n" );
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document.write( "Now multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2i ALIGN=MIDDLE  ALT=\"2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > by its reciprocal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%282i%29 ALIGN=MIDDLE  ALT=\"1%2F%282i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%281%2F%282i%29%29 ALIGN=MIDDLE  ALT=\"%282i%29%281%2F%282i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%2F%282i%29 ALIGN=MIDDLE  ALT=\"%282i%29%2F%282i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%282%29i%29%2F%28cross%282%29i%29 ALIGN=MIDDLE  ALT=\"%28cross%282%29i%29%2F%28cross%282%29i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Fi ALIGN=MIDDLE  ALT=\"i%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%2Ai%29%2F%28i%2Ai%29 ALIGN=MIDDLE  ALT=\"%28i%2Ai%29%2F%28i%2Ai%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by \"i\" to make the denominator real (this doesn't change the expression)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28i%5E2%29%2F%28i%5E2%29 ALIGN=MIDDLE  ALT=\"%28i%5E2%29%2F%28i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=%28sqrt%28-1%29%29%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=%28sqrt%28-1%29%29%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%281%2F%282i%29%29=1 ALIGN=MIDDLE  ALT=\"%282i%29%281%2F%282i%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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