document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173218>Question 173218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What does the product (4+7i)(2-5i) equal?\r<BR>\n" );
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document.write( "What does the quotient (1+4i)/(5-2i) equal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128050 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=128050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B7i%29%2A%282-5i%29 ALIGN=MIDDLE  ALT=\"%284%2B7i%29%2A%282-5i%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=%284%29%282%29%2B%284%29%28-5i%29%2B%287i%29%282%29%2B%287i%29%28-5i%29 ALIGN=MIDDLE  ALT=\"%284%29%282%29%2B%284%29%28-5i%29%2B%287i%29%282%29%2B%287i%29%28-5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-20i%2B14i-35i%5E2 ALIGN=MIDDLE  ALT=\"8-20i%2B14i-35i%5E2\"   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=8-20i%2B14i-35%28-1%29 ALIGN=MIDDLE  ALT=\"8-20i%2B14i-35%28-1%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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   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=8-20i%2B14i%2B35 ALIGN=MIDDLE  ALT=\"8-20i%2B14i%2B35\"   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=43-6i ALIGN=MIDDLE  ALT=\"43-6i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B7i%29%2A%282-5i%29=43-6i ALIGN=MIDDLE  ALT=\"%284%2B7i%29%2A%282-5i%29=43-6i\"   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=43 ALIGN=MIDDLE  ALT=\"a=43\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B4i%29%2F%285-2i%29 ALIGN=MIDDLE  ALT=\"%281%2B4i%29%2F%285-2i%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%2B4i%29%2F%285-2i%29%29%28%285%2B2i%29%2F%285%2B2i%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2B4i%29%2F%285-2i%29%29%28%285%2B2i%29%2F%285%2B2i%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%2B2i%29%2F%285%2B2i%29 ALIGN=MIDDLE  ALT=\"%285%2B2i%29%2F%285%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is the complex conjugate of the denominator).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2B4i%29%285%2B2i%29%29%2F%28%285-2i%29%285%2B2i%29%29 ALIGN=MIDDLE  ALT=\"%28%281%2B4i%29%285%2B2i%29%29%2F%28%285-2i%29%285%2B2i%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%281%29%285%29%2B%281%29%282i%29%2B%284i%29%285%29%2B%284i%29%282i%29%29%2F%28%285-2i%29%285%2B2i%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%281%29%285%29%2B%281%29%282i%29%2B%284i%29%285%29%2B%284i%29%282i%29%29%2F%28%285%29%285%29%2B%285%29%282i%29%2B%28-2i%29%285%29%2B%28-2i%29%282i%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=%285%2B2i%2B20i%2B8i%5E2%29%2F%2825%2B10i-10i-4i%5E2%29 ALIGN=MIDDLE  ALT=\"%285%2B2i%2B20i%2B8i%5E2%29%2F%2825%2B10i-10i-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=%28-3%2B22i%29%2F%2829%29 ALIGN=MIDDLE  ALT=\"%28-3%2B22i%29%2F%2829%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=-3%2F29%2B%2822%2F29%29%2Ai ALIGN=MIDDLE  ALT=\"-3%2F29%2B%2822%2F29%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B4i%29%2F%285-2i%29=-3%2F29%2B%2822%2F29%29%2Ai ALIGN=MIDDLE  ALT=\"%281%2B4i%29%2F%285-2i%29=-3%2F29%2B%2822%2F29%29%2Ai\"   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%2F29 ALIGN=MIDDLE  ALT=\"a=-3%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=22%2F29 ALIGN=MIDDLE  ALT=\"b=22%2F29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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