document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065588>Question 1065588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For which of the following operations will the complex numbers (4-3i) and (1+2i) produce a real solution? Find the solution.\r<BR>\n" );
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document.write( "A) Addition<BR>\n" );
document.write( "B) Subtraction<BR>\n" );
document.write( "C) Multiplication<BR>\n" );
document.write( "D) Division\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680779 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=680779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you are not sure, try each of them and see.\r<BR>\n" );
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document.write( "Addition will give you an imaginary component, and so will subtraction.\r<BR>\n" );
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document.write( "Multiplication?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-3i%2B2i-6i%5E2 ALIGN=MIDDLE  ALT=\"4-3i%2B2i-6i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "No.  You have the imaginary, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i ALIGN=MIDDLE  ALT=\"-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > as part of the number.\r<BR>\n" );
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document.write( "Division?<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-3i%29%2F%281%2B2i%29 ALIGN=MIDDLE  ALT=\"%284-3i%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=%28%284-3i%29%2F%281%2B2i%29%29%28%281-2i%29%2F%281-2i%29%29 ALIGN=MIDDLE  ALT=\"%28%284-3i%29%2F%281%2B2i%29%29%28%281-2i%29%2F%281-2i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simply multiplication by 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-3i-8i%2B6i%5E2%29%2F%281-4i%5E2%29 ALIGN=MIDDLE  ALT=\"%284-3i-8i%2B6i%5E2%29%2F%281-4i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------but you still will have an imaginary component in the numerator.<BR>\n" );
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document.write( "You can also try the reciprocal and see what it will be, but...<BR>\n" );
document.write( "You try it.<BR>\n" );
document.write( "Unless this gives you a fully REAL result,  none of the choices will produce a real solution. </SPAN>\n" );
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