document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133322>Question 1133322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 3 cubic roots of unity (1 + 0i) in complex standard form.\r<BR>\n" );
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document.write( "the 0 is a zero, not a theta<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750518 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=750518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume the cube root of 1 is z, that is,<BR>\n" );
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document.write( "z = 1^(1/3)<BR>\n" );
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document.write( "now cube both sides of the =<BR>\n" );
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document.write( "z^3 = 1<BR>\n" );
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document.write( "rewrite as<BR>\n" );
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document.write( "z^3 -1 = 0<BR>\n" );
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document.write( "this cubic can be factored <BR>\n" );
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document.write( "(z-1)(z^2 +z +1) = 0<BR>\n" );
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document.write( "use quadratic formula<BR>\n" );
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document.write( "z = -1 +square root(1^2 -4**1)/2*1 = -(1/2) +i * square root(3)/2<BR>\n" );
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document.write( "z = -1 -square root(1^2 -4**1)/2*1 = -(1/2) -i * square root(3)/2 <BR>\n" );
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document.write( "z = 1<BR>\n" );
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document.write( "The 3 cubic roots of unity (1 + 0i) in complex standard form are<BR>\n" );
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document.write( "1+0i, (-1+i*square root(3))/2, (-1-i*square root(3))/2<BR>\n" );
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