document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081986>Question 1081986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please answer this question for finding the complex number z = x + yi that satisfies the equation (1+3i)z + (4-2i)z = 10+4i<BR>\n" );
document.write( "Thank you so much if you help!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696045 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=696045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1+3i)z + (4-2i)z = 10+4i<BR>\n" );
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document.write( "factor z on left side of =<BR>\n" );
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document.write( "z(1+3i +4-2i) = 10+4i<BR>\n" );
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document.write( "z(5+i) = 10+4i<BR>\n" );
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document.write( "divide both sides of = by (5+i)<BR>\n" );
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document.write( "z = (10+4i) / (5+i)<BR>\n" );
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document.write( "multiply the numerator and denominator by (5-i)<BR>\n" );
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document.write( "z = ((10+4i)*(5-i)) / ((5+i)*(5-i))<BR>\n" );
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document.write( "z = (10+4i)*(5-i) / 26<BR>\n" );
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document.write( "Note that -i^2 = -(-1) = 1<BR>\n" );
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document.write( "(10+4i) and 26 are divisible by 2<BR>\n" );
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document.write( "z = (5+2i)*(5-i) / 13<BR>\n" );
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document.write( "z = (25+10i-5i-2i^2) / 13<BR>\n" );
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document.write( "z = (27+5i) / 13<BR>\n" );
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