document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=540721>Question 540721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If arg((z-w)/(z-w^2)) =0,then prove that re(z)=-1/2,where (w and w^2 are non real cube roots of unity) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353870 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=353870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the argument of some complex number is 0, then the number must be a positive real number. Also, the numerator (z - omega) can be set to zero. We have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \omega = -\frac{1}{2} + \frac{\sqrt{3}}{2}i \Rightarrow Re(\omega) = -\frac{1}{2}\">\r<BR>\n" );
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document.write( "Since we want <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE Re(z - \omega) = 0\"> we set <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE Re(z) = \frac{1}{2}\">. </SPAN>\n" );
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