document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124825>Question 124825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give answer in a + bi form.\r<BR>\n" );
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document.write( "4 - 5i / 2 + 3i<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 #91487 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need to remember the 'difference of two squares' factorization: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29=a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What we want to accomplish is to get that pesky i out of our denominator.  Using the difference of two squares idea, we see that we can accomplish this quite nicely by multiplying the denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-3i ALIGN=MIDDLE  ALT=\"2-3i\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Of course if we multiply the denominator by something, we must multiply the numerator by the same thing, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284-5i%29%2F%282%2B3i%29%29%28%282-3i%29%2F%282-3i%29%29 ALIGN=MIDDLE  ALT=\"%28%284-5i%29%2F%282%2B3i%29%29%28%282-3i%29%2F%282-3i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the difference of two squares on the denominator, and FOIL on the numerator we obtain:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288-12i-10i%2B15i%5E2%29%2F%284-9i%5E2%29 ALIGN=MIDDLE  ALT=\"%288-12i-10i%2B15i%5E2%29%2F%284-9i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, collect terms remembering that <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=%28%28-7%29-22i%29%2F13 ALIGN=MIDDLE  ALT=\"%28%28-7%29-22i%29%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In <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;\" > form you have:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%287%2F13%29-%2822%2F13%29i ALIGN=MIDDLE  ALT=\"-%287%2F13%29-%2822%2F13%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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