document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181502>Question 1181502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the roots of (z^2) - z(1 + i) + 5i = 0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811406 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "roots of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+-+z%281+%2B+i%29+%2B+5i+=+0 ALIGN=MIDDLE  ALT=\"z%5E2+-+z%281+%2B+i%29+%2B+5i+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......... substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%2Byi ALIGN=MIDDLE  ALT=\"z=x%2Byi\"   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=%28x%2Byi%29%5E2+-+%28x%2Byi%29%281+%2B+i%29+%2B+5i+=+0 ALIGN=MIDDLE  ALT=\"%28x%2Byi%29%5E2+-+%28x%2Byi%29%281+%2B+i%29+%2B+5i+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...expand\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2xy%2Ai%2B%28yi%29%5E2+-+%28x%2Bx%2Ai%2Byi%2By%2Ai%5E2%29%2B+5i+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2xy%2Ai%2B%28yi%29%5E2+-+%28x%2Bx%2Ai%2Byi%2By%2Ai%5E2%29%2B+5i+=+0\"   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=x%5E2%2B2xy%2Ai%2B%28yi%29%5E2+-+%28x%2Bx%2Ai%2Byi-y%29%2B+5i+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2xy%2Ai%2B%28yi%29%5E2+-+%28x%2Bx%2Ai%2Byi-y%29%2B+5i+=+0\"   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=x%5E2%2B2xy%2Ai%2B%28y%5E2i%5E2%29+-+x-x%2Ai-yi%2By%2B+5i+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2xy%2Ai%2B%28y%5E2i%5E2%29+-+x-x%2Ai-yi%2By%2B+5i+=+0\"   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=x%5E2%2B2xy%2Ai-y%5E2+-+x-x%2Ai-yi%2By%2B+5i+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2xy%2Ai-y%5E2+-+x-x%2Ai-yi%2By%2B+5i+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........combine real parts and imaginary parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-y%5E2+-x%2By%29%2B2xy%2Ai-x%2Ai-yi%2B+5i=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-y%5E2+-x%2By%29%2B2xy%2Ai-x%2Ai-yi%2B+5i=0\"   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=%28x%5E2-y%5E2+-x%2By%29-i%282xy-x-y%2B5%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-y%5E2+-x%2By%29-i%282xy-x-y%2B5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Complex numbers can be equal only if their real and imaginary parts are equal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2+-x%2By=0 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2+-x%2By=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy-x-y%2B5=0 ALIGN=MIDDLE  ALT=\"2xy-x-y%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2<BR>\n" );
document.write( "-------------------solve this system \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy-x=y-5 ALIGN=MIDDLE  ALT=\"2xy-x=y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >....eq.2, solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=%282y-1%29x=y-5 ALIGN=MIDDLE  ALT=\"%282y-1%29x=y-5\"   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=x=%28y-5%29%2F%282y-1%29 ALIGN=MIDDLE  ALT=\"x=%28y-5%29%2F%282y-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-5%29%2F%282y-1%29%29%5E2-y%5E2+-%28y-5%29%2F%282y-1%29%2By=0 ALIGN=MIDDLE  ALT=\"%28%28y-5%29%2F%282y-1%29%29%5E2-y%5E2+-%28y-5%29%2F%282y-1%29%2By=0\"   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%28y+-+2%29+%28y+%2B+1%29%29%2F%282+y+-+1%29+=+0 ALIGN=MIDDLE  ALT=\"%28%28y+-+2%29+%28y+%2B+1%29%29%2F%282+y+-+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >} .........zeros are in numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+2%29+%28y+%2B+1%29=0 ALIGN=MIDDLE  ALT=\"%28y+-+2%29+%28y+%2B+1%29=0\"   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=y=2+ ALIGN=MIDDLE  ALT=\"y=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%282-5%29%2F%282%2A2-1%29=-3%2F3=-1 ALIGN=MIDDLE  ALT=\"x=%282-5%29%2F%282%2A2-1%29=-3%2F3=-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=x=%28-1-5%29%2F%282%28-1%29-1%29=-6%2F-3=2 ALIGN=MIDDLE  ALT=\"x=%28-1-5%29%2F%282%28-1%29-1%29=-6%2F-3=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute back  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%2Byi ALIGN=MIDDLE  ALT=\"z=x%2Byi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and roots are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B1%5D=2-i ALIGN=MIDDLE  ALT=\"z%5B1%5D=2-i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5B2%5D=-1%2B2i ALIGN=MIDDLE  ALT=\"z%5B2%5D=-1%2B2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );