document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990393>Question 990393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (3-2i)(1+i) + |3+4i|. <BR>\n" );
document.write( "Turn this into a+bi form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610477 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52768)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=610477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1. &nbsp;Let me calculate this term first, &nbsp;(3-2i)(1+i).\r<BR>\n" );
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document.write( "You need simply open parentheses, &nbsp;make multiplications, &nbsp;collect common terms and use the fact that &nbsp;i*i = <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;\" > = -1. &nbsp;So, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-2i%29%281%2Bi%29 ALIGN=MIDDLE  ALT=\"%283-2i%29%281%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A1+-2i%2A1+%2B+3%2Ai+%2B%28-2i%29%2Ai ALIGN=MIDDLE  ALT=\"3%2A1+-2i%2A1+%2B+3%2Ai+%2B%28-2i%29%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+-+2i+%2B+3i+-2i%5E2 ALIGN=MIDDLE  ALT=\"3+-+2i+%2B+3i+-2i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3 + i -2*(-1) = 3 + i + 2 = 5 + i. \r<BR>\n" );
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document.write( "Very good.\r<BR>\n" );
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document.write( "2. &nbsp;Now let consider this term, &nbsp;|3 + 4i|. \r<BR>\n" );
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document.write( "It is the modulus of the complex number &nbsp;3 + 4i. \r<BR>\n" );
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document.write( "As you probably know, &nbsp;the modulus is the square root of the sum of squares of the components: &nbsp;r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2+%2B+4%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2+%2B+4%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289+%2B+16%29 ALIGN=MIDDLE  ALT=\"sqrt%289+%2B+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5.\r<BR>\n" );
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document.write( "So, &nbsp;the modulus &nbsp;<B>r</B>&nbsp; is, &nbsp;in our case, &nbsp;simply the real number &nbsp;5.\r<BR>\n" );
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document.write( "Very good.\r<BR>\n" );
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document.write( "3. &nbsp;Now, &nbsp;the sum (3-2i)(1+i) + |3 + 4i| = (5 + i) + 5 = 10 + i.\r<BR>\n" );
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document.write( "That is all. \r<BR>\n" );
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document.write( "Congratulations!\r<BR>\n" );
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document.write( "To learn more on complex numbers, you can read my lessons in this site\r<BR>\n" );
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document.write( "It is free of charge.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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