document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192058>Question 192058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The complex number 13 + i can be factored into the product of 1 + 2i and what other complex number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144116 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=144116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since 13 + i can be factored where one factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2i ALIGN=MIDDLE  ALT=\"1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13+%2B+i=%281%2B2i%29%2Ax ALIGN=MIDDLE  ALT=\"13+%2B+i=%281%2B2i%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"x\" is the other factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13+%2B+i=%281%2B2i%29%2Ax ALIGN=MIDDLE  ALT=\"13+%2B+i=%281%2B2i%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813+%2B+i%29%2F%281%2B2i%29=x ALIGN=MIDDLE  ALT=\"%2813+%2B+i%29%2F%281%2B2i%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2i ALIGN=MIDDLE  ALT=\"1%2B2i\"   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=x=%2813+%2B+i%29%2F%281%2B2i%29 ALIGN=MIDDLE  ALT=\"x=%2813+%2B+i%29%2F%281%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "So the other factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813+%2B+i%29%2F%281%2B2i%29 ALIGN=MIDDLE  ALT=\"%2813+%2B+i%29%2F%281%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Let's simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813+%2B+i%29%2F%281%2B2i%29 ALIGN=MIDDLE  ALT=\"%2813+%2B+i%29%2F%281%2B2i%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=%2813%2Bi%29%2F%281%2B2i%29 ALIGN=MIDDLE  ALT=\"%2813%2Bi%29%2F%281%2B2i%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%2813%2Bi%29%2F%281%2B2i%29%29%28%281-2i%29%2F%281-2i%29%29 ALIGN=MIDDLE  ALT=\"%28%2813%2Bi%29%2F%281%2B2i%29%29%28%281-2i%29%2F%281-2i%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=%281-2i%29%2F%281-2i%29 ALIGN=MIDDLE  ALT=\"%281-2i%29%2F%281-2i%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%2813%2Bi%29%281-2i%29%29%2F%28%281%2B2i%29%281-2i%29%29 ALIGN=MIDDLE  ALT=\"%28%2813%2Bi%29%281-2i%29%29%2F%28%281%2B2i%29%281-2i%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%2813%29%281%29%2B%2813%29%28-2i%29%2B%28i%29%281%29%2B%28i%29%28-2i%29%29%2F%28%281%2B2i%29%281-2i%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%2813%29%281%29%2B%2813%29%28-2i%29%2B%28i%29%281%29%2B%28i%29%28-2i%29%29%2F%28%281%29%281%29%2B%281%29%28-2i%29%2B%282i%29%281%29%2B%282i%29%28-2i%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=%2813-26i%2Bi-2i%5E2%29%2F%281-2i%2B2i-4i%5E2%29 ALIGN=MIDDLE  ALT=\"%2813-26i%2Bi-2i%5E2%29%2F%281-2i%2B2i-4i%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=%2815-25i%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%2815-25i%29%2F%285%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=%2815%29%2F%285%29%2B%28%28-25%29%2F%285%29%29i ALIGN=MIDDLE  ALT=\"%2815%29%2F%285%29%2B%28%28-25%29%2F%285%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=3-5i ALIGN=MIDDLE  ALT=\"3-5i\"   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=%2813%2Bi%29%2F%281%2B2i%29=3-5i ALIGN=MIDDLE  ALT=\"%2813%2Bi%29%2F%281%2B2i%29=3-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2813%2Bi%29%2F%281%2B2i%29 ALIGN=MIDDLE  ALT=\"x=%2813%2Bi%29%2F%281%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3-5i ALIGN=MIDDLE  ALT=\"x=3-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the other factor is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-5i ALIGN=MIDDLE  ALT=\"3-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Bi=%281%2B2i%29%283-5i%29 ALIGN=MIDDLE  ALT=\"13%2Bi=%281%2B2i%29%283-5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: you can check this by multiplying the given factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2i ALIGN=MIDDLE  ALT=\"1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-5i ALIGN=MIDDLE  ALT=\"3-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Bi ALIGN=MIDDLE  ALT=\"13%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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