document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189232>Question 189232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the complex number  \r<BR>\n" );
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document.write( "2-i<BR>\n" );
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document.write( "5+i \r<BR>\n" );
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document.write( "in the usual  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 #141963 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=141963\">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=%282-i%29%2F%285%2Bi%29 ALIGN=MIDDLE  ALT=\"%282-i%29%2F%285%2Bi%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%282-i%29%2F%285%2Bi%29%29%28%285-i%29%2F%285-i%29%29 ALIGN=MIDDLE  ALT=\"%28%282-i%29%2F%285%2Bi%29%29%28%285-i%29%2F%285-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-i%29%2F%285-i%29 ALIGN=MIDDLE  ALT=\"%285-i%29%2F%285-i%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%282-i%29%285-i%29%29%2F%28%285%2Bi%29%285-i%29%29 ALIGN=MIDDLE  ALT=\"%28%282-i%29%285-i%29%29%2F%28%285%2Bi%29%285-i%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=%28%282%29%285%29%2B%282%29%28-i%29%2B%28-i%29%285%29%2B%28-i%29%28-i%29%29%2F%28%285%2Bi%29%285-i%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%29%285%29%2B%282%29%28-i%29%2B%28-i%29%285%29%2B%28-i%29%28-i%29%29%2F%28%285%29%285%29%2B%285%29%28-i%29%2B%28i%29%285%29%2B%28i%29%28-i%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the denominator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810-2i-5i%2Bi%5E2%29%2F%2825-5i%2B5i-i%5E2%29 ALIGN=MIDDLE  ALT=\"%2810-2i-5i%2Bi%5E2%29%2F%2825-5i%2B5i-i%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=%289-7i%29%2F%2826%29 ALIGN=MIDDLE  ALT=\"%289-7i%29%2F%2826%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=%289%29%2F%2826%29%2B%28%28-7%29%2F%2826%29%29i ALIGN=MIDDLE  ALT=\"%289%29%2F%2826%29%2B%28%28-7%29%2F%2826%29%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=9%2F26-%287%2F26%29i ALIGN=MIDDLE  ALT=\"9%2F26-%287%2F26%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=%282-i%29%2F%285%2Bi%29=9%2F26-%287%2F26%29i ALIGN=MIDDLE  ALT=\"%282-i%29%2F%285%2Bi%29=9%2F26-%287%2F26%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So the expression is now 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=9%2F26 ALIGN=MIDDLE  ALT=\"a=9%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-7%2F26 ALIGN=MIDDLE  ALT=\"b=-7%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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