document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120862>Question 120862</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/495078816/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the expression and write the result in the form a + bi. \r<BR>\n" );
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document.write( "1/8+10i - 1/8+10i  = _____ + _______i\r<BR>\n" );
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document.write( "I do not know how to divide complex numbers.  Note that that 8+10i is the numerator in both equations.  \r<BR>\n" );
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document.write( "I would greatly appreciate your help!!  Thank you so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88658 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=88658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm pretty sure you meant to say 8 + 10i is the <i>denominator</i> of both <i>fractions</i>, and your problem actually looks like:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%288%2B10i%29%29-%281%2F%288%2B10i%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%288%2B10i%29%29-%281%2F%288%2B10i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Just like working with any other fractions, if the denominators are equal, then you simply add the numerators.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-1%29%2F%288%2B10i%29=0 ALIGN=MIDDLE  ALT=\"%281-1%29%2F%288%2B10i%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We could have made this a little more complicated by using a process called rationalizing the denominators, but the result will still be the same.  Watch closely.\r<BR>\n" );
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document.write( "First thing is to remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   Having said that, we are now going to multiply each of the fractions by 1, in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288-10i%29%2F%288-10i%29 ALIGN=MIDDLE  ALT=\"%288-10i%29%2F%288-10i%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=%28%288-10i%29%2F%288-10i%29%29%281%2F%288%2B10i%29%29-%28%288-10i%29%2F%288-10i%29%29%281%2F%288%2B10i%29%29 ALIGN=MIDDLE   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%288-10i%29%288%2B10i%29%29=64-%28-100%29 ALIGN=MIDDLE  ALT=\"%28%288-10i%29%288%2B10i%29%29=64-%28-100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), so our denominator becomes 164, giving us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288-10i%29-%288-10i%29%29%2F164 ALIGN=MIDDLE  ALT=\"%28%288-10i%29-%288-10i%29%29%2F164\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, to add complex numbers, you just add the real parts to the real parts and the imaginary parts to the imaginary parts:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bbi%29%2B%28c%2Bdi%29=%28a%2Bb%29%2B%28c%2Bd%29i ALIGN=MIDDLE  ALT=\"%28a%2Bbi%29%2B%28c%2Bdi%29=%28a%2Bb%29%2B%28c%2Bd%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In our problem, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288-8%29-%2810-10%29i%29%2F164 ALIGN=MIDDLE  ALT=\"%28%288-8%29-%2810-10%29i%29%2F164\"   DISABLED_style= \"max-width:90%; height:auto;\" > giving us:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F164=0 ALIGN=MIDDLE  ALT=\"0%2F164=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you need to express 0 in complex number (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bbi%29 ALIGN=MIDDLE  ALT=\"%28a%2Bbi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) form, then you would write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B0i%29 ALIGN=MIDDLE  ALT=\"%280%2B0i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hope that helps.\r<BR>\n" );
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