document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159832>Question 159832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Can you please help with imaginary numbers?<BR>\n" );
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document.write( "Simplify<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%2B4i%29%2F%286-2i%29+ ALIGN=MIDDLE  ALT=\"+%283%2B4i%29%2F%286-2i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Put in complex number form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2B+bi+ ALIGN=MIDDLE  ALT=\"+a+%2B+bi+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Thanks ahead of time, Levi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117851 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=117851\">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=+%283%2B4i%29%2F%286-2i%29+ ALIGN=MIDDLE  ALT=\"+%283%2B4i%29%2F%286-2i%29+\"   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=+%28%283%2B4i%29%2F%286-2i%29%29%28%286%2B2i%29%2F%286%2B2i%29%29+ ALIGN=MIDDLE  ALT=\"+%28%283%2B4i%29%2F%286-2i%29%29%28%286%2B2i%29%2F%286%2B2i%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both numerator and denominator by conjugate of the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2i ALIGN=MIDDLE  ALT=\"6-2i\"   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=+%28%283%2B4i%29%286%2B2i%29%29%2F%28%286-2i%29%286%2B2i%29%29 ALIGN=MIDDLE  ALT=\"+%28%283%2B4i%29%286%2B2i%29%29%2F%28%286-2i%29%286%2B2i%29%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=+%2818%2B30i%2B8i%5E2%29%2F%2836-4i%5E2%29 ALIGN=MIDDLE  ALT=\"+%2818%2B30i%2B8i%5E2%29%2F%2836-4i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2818%2B30i-8%29%2F%2836%2B4%29 ALIGN=MIDDLE  ALT=\"+%2818%2B30i-8%29%2F%2836%2B4%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 -1 and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%2B30i%29%2F%2840%29 ALIGN=MIDDLE  ALT=\"+%2810%2B30i%29%2F%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F40%2B%2830%2F40%29i ALIGN=MIDDLE  ALT=\"10%2F40%2B%2830%2F40%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%2B%283%2F4%29i ALIGN=MIDDLE  ALT=\"1%2F4%2B%283%2F4%29i\"   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=+%283%2B4i%29%2F%286-2i%29+ ALIGN=MIDDLE  ALT=\"+%283%2B4i%29%2F%286-2i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%2B%283%2F4%29i ALIGN=MIDDLE  ALT=\"1%2F4%2B%283%2F4%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%283%2B4i%29%2F%286-2i%29+=+1%2F4%2B%283%2F4%29i ALIGN=MIDDLE  ALT=\"+%283%2B4i%29%2F%286-2i%29+=+1%2F4%2B%283%2F4%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how the result is in standard form <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;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1%2F4 ALIGN=MIDDLE  ALT=\"a=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3%2F4 ALIGN=MIDDLE  ALT=\"b=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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