document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189902>Question 189902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression and write the result in standard a+bi form. Show all work.\r<BR>\n" );
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document.write( "        1/3+i= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142490 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=142490\">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=%281%29%2F%283%2Bi%29 ALIGN=MIDDLE  ALT=\"%281%29%2F%283%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%281%29%2F%283%2Bi%29%29%28%283-i%29%2F%283-i%29%29 ALIGN=MIDDLE  ALT=\"%28%281%29%2F%283%2Bi%29%29%28%283-i%29%2F%283-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=%283-i%29%2F%283-i%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%283-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%281%29%283-i%29%29%2F%28%283%2Bi%29%283-i%29%29 ALIGN=MIDDLE  ALT=\"%28%281%29%283-i%29%29%2F%28%283%2Bi%29%283-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=%283-i%29%2F%28%283%2Bi%29%283-i%29%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%28%283%2Bi%29%283-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-i%29%2F%289-3i%2B3i-i%5E2%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%289-3i%2B3i-i%5E2%29\"   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=%283-i%29%2F%289-3i%2B3i-%28-1%29%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%289-3i%2B3i-%28-1%29%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\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-i%29%2F%289-3i%2B3i%2B1%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%289-3i%2B3i%2B1%29\"   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=%283-i%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%2810%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=%283%29%2F%2810%29%2B%28%28-1%29%2F%2810%29%29i ALIGN=MIDDLE  ALT=\"%283%29%2F%2810%29%2B%28%28-1%29%2F%2810%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=3%2F10-%281%2F10%29i ALIGN=MIDDLE  ALT=\"3%2F10-%281%2F10%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=%281%29%2F%283%2Bi%29=3%2F10-%281%2F10%29i ALIGN=MIDDLE  ALT=\"%281%29%2F%283%2Bi%29=3%2F10-%281%2F10%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=3%2F10 ALIGN=MIDDLE  ALT=\"a=3%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1%2F10 ALIGN=MIDDLE  ALT=\"b=-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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