document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72133>Question 72133</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0673459608/algebrahomeworkh>Advanced Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Write 5/(6-2i) in a+bi form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51568 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51568\">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=5%2F%286-2i%29 ALIGN=MIDDLE  ALT=\"5%2F%286-2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "to get this to the form a + bi begin by multiplying the given term by:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+%2B+2i%29%2F%286%2B2i%29 ALIGN=MIDDLE  ALT=\"%286+%2B+2i%29%2F%286%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Note that this is equivalent to multiplying the given term by 1 because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+%2B+2i%29%2F%286%2B2i%29 ALIGN=MIDDLE  ALT=\"%286+%2B+2i%29%2F%286%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "equals 1.<BR>\n" );
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document.write( "The numerator multiplication of the 5 times the (6 + 2i) results in 30 + 20i.<BR>\n" );
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document.write( "Then the denominator multiplication of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286+-+2i%29%2A%286+%2B+2i%29 ALIGN=MIDDLE  ALT=\"%286+-+2i%29%2A%286+%2B+2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36+-+12i+%2B+12i+-4%2Ai%5E2 ALIGN=MIDDLE  ALT=\"+36+-+12i+%2B+12i+-4%2Ai%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The -12i and + 12i cancel each other out. Then recall that <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;\" > by definition is -1.<BR>\n" );
document.write( "Substituting -1 for <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;\" > leads to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+-4%2A%28-1%29+=+36+%2B+4+=+40 ALIGN=MIDDLE  ALT=\"36+-4%2A%28-1%29+=+36+%2B+4+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the denominator ... +40.  From above the numerator is 30 + 20i. So the answer is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830%2B20%2Ai%29%2F40+=+%283%2F4%29+%2B+%281%2F2%29%2Ai ALIGN=MIDDLE  ALT=\"%2830%2B20%2Ai%29%2F40+=+%283%2F4%29+%2B+%281%2F2%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The answer to your problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29+%2B+%281%2F2%29%2Ai ALIGN=MIDDLE  ALT=\"%283%2F4%29+%2B+%281%2F2%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%283%2F4%29 ALIGN=MIDDLE  ALT=\"a+=+%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+%281%2F2%29 ALIGN=MIDDLE  ALT=\"b=+%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand complex numbers. Notice how you can eliminate complex<BR>\n" );
document.write( "numbers in the denominator by multiplying the denominator by the same complex number with <BR>\n" );
document.write( "a change in signs between the real and imaginary parts. This converts the denominator<BR>\n" );
document.write( "to a real number. <BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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