document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725195>Question 725195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> z^3=3-3i\r<BR>\n" );
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document.write( "            module       argument         exponencial representation <BR>\n" );
document.write( "       <BR>\n" );
document.write( "solution 1 \r<BR>\n" );
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document.write( "solution 2\r<BR>\n" );
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document.write( "solution 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444008 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=444008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can't really tell what your problem is.<BR>\n" );
document.write( "The z^3 = 3-3i seems to indicate you want to solve for \"z\"<BR>\n" );
document.write( "which would be the three cube roots of 3-3i.<BR>\n" );
document.write( "If that is true:\r<BR>\n" );
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document.write( "z^3=3-3i <BR>\n" );
document.write( "module argument exponential representation <BR>\n" );
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document.write( "r = sqrt(3^2+3^2) = 3sqrt(2)<BR>\n" );
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document.write( "theta = tan^-1(-3/3) = tan^-1(-1) = (3/4)pi<BR>\n" );
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document.write( "3 -3i = 3sqrt(2)(cis[(3/4)pi]<BR>\n" );
document.write( "z = (3sqrt(2))^(1/3)*(cis(3/4)pi+(2npi))<BR>\n" );
document.write( "Let n = 0 to get z = (3sqrt(2))^(1/3)cis((1/4)pi)<BR>\n" );
document.write( "If n = 1 get z = (3sqrt(2))^(1/3)cis((1/4)pi+(2/3)pi)<BR>\n" );
document.write( "If n = 2 get z = (3sqrt(2))^(1/3)cis((1/4)pi + (4/3)pi)\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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