document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=399468>Question 399468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show an argand diagram of the three roots of the equation<BR>\n" );
document.write( "Z^3 -1=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282878 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=282878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Use the difference of two cubes factorization:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^3\ -\ b^3\ =\ (a\ -\ b)(a^2\ +\ ab\ +\ b^2)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ z^3\ -\ 1\ =\ (z\ -\ 1)(z^2\ +\ z\ +\ 1)\">\r<BR>\n" );
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document.write( "One root is 1, but in complex form that would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large z\ =\ 1\ +\ 0i\">.  Therefore, plot the point (1,0) on your <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x,yi\"> axes.\r<BR>\n" );
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document.write( "For the other two roots, solve:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ z^2\ +\ z\ +\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "using the quadratic formula to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ z\ =\ \frac{-1\ \pm\ i sqrt{3}}{2}\">\r<BR>\n" );
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document.write( "Hence, plot <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\frac{1}{2},\frac{i\sqrt{3}}{2}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\frac{1}{2},-\frac{i\sqrt{3}}{2}\right)\"> on your <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x,yi\"> axes.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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