document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=144741>Question 144741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Multiply the complex numbers.\r<BR>\n" );
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document.write( "(5 + 2i)(2 - i)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105471 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=105471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B2i%29%282-i%29 ALIGN=MIDDLE  ALT=\"%285%2B2i%29%282-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Now let's FOIL the expression\r<BR>\n" );
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document.write( "Remember, when you FOIL an expression, you follow this procedure:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%285%29%2B2i%29%28highlight%282%29-i%29 ALIGN=MIDDLE  ALT=\"%28highlight%285%29%2B2i%29%28highlight%282%29-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">F</font>irst terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2A%282%29=10 ALIGN=MIDDLE  ALT=\"%285%29%2A%282%29=10\"   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=%28highlight%285%29%2B2i%29%282%2Bhighlight%28-i%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%285%29%2B2i%29%282%2Bhighlight%28-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">O</font>uter terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%2A%28-1i%29=-5i ALIGN=MIDDLE  ALT=\"%285%29%2A%28-1i%29=-5i\"   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=%285%2Bhighlight%282i%29%29%28highlight%282%29-i%29 ALIGN=MIDDLE  ALT=\"%285%2Bhighlight%282i%29%29%28highlight%282%29-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">I</font>nner terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%2A%282%29=4i ALIGN=MIDDLE  ALT=\"%282i%29%2A%282%29=4i\"   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=%285%2Bhighlight%282i%29%29%282%2Bhighlight%28-i%29%29 ALIGN=MIDDLE  ALT=\"%285%2Bhighlight%282i%29%29%282%2Bhighlight%28-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">L</font>ast terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%2A%28-1i%29=-2i%5E2=-2%28-1%29=2 ALIGN=MIDDLE  ALT=\"%282i%29%2A%28-1i%29=-2i%5E2=-2%28-1%29=2\"   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=10-5i%2B4i%2B2 ALIGN=MIDDLE  ALT=\"10-5i%2B4i%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now collect every term to make a single expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-i ALIGN=MIDDLE  ALT=\"12-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms\r<BR>\n" );
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document.write( "---------------------\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B2i%29%282-i%29 ALIGN=MIDDLE  ALT=\"%285%2B2i%29%282-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > foils and simplifies to  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12-i ALIGN=MIDDLE  ALT=\"12-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B2i%29%282-i%29=12-i ALIGN=MIDDLE  ALT=\"%285%2B2i%29%282-i%29=12-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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