document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=582098>Question 582098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve:  (1-4i)/(2+3i)\r<BR>\n" );
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document.write( "i indicates a number that is imaginary ( sqrt of -1)\r<BR>\n" );
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document.write( "thanks so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371935 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you solve:  (1-4i)/(2+3i)<BR>\n" );
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document.write( "You don't solve it.  There's no variable to solve for.<BR>\n" );
document.write( "The goal is to rationalize the denominator, ie, get the i out of it.<BR>\n" );
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document.write( "(1-4i)/(2+3i)<BR>\n" );
document.write( "Multiply the NUM and DEN by the conjugate of the DEN, 2-3i<BR>\n" );
document.write( "= (1-4i)(2-3i)/((2+3i)(2-3i))<BR>\n" );
document.write( "= (2 - 11i +12i^2)/(4 - 9i^2)<BR>\n" );
document.write( "= (2 - 11i - 12)/(4 + 9)<BR>\n" );
document.write( "= (-10 - 11i)/13<BR>\n" );
document.write( "or -10/13 - i(11/13)<BR>\n" );
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