document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181459>Question 1181459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> z = 2 ( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } )\r<BR>\n" );
document.write( "\n" );
document.write( "What will Z^4 be equal to </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811358 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=811358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+2%28cos%28pi%2F3%29%2Bi%2Asin%28pi%2F3%29%29+=+2%28cis%28pi%2F3%29%29%29 ALIGN=MIDDLE  ALT=\"z+=+2%28cos%28pi%2F3%29%2Bi%2Asin%28pi%2F3%29%29+=+2%28cis%28pi%2F3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The modulus (\"magnitude\") is 2; the angle is pi/3.<br><BR>\n" );
document.write( "DeMoivre's Theorem says to raise the complex number to the n-th power you raise the modulus to the n-th power and multiply the angle by n.<br><BR>\n" );
document.write( "You can do the simple calculations to find the answer to your problem.<br><BR>\n" );
document.write( "Here are a couple of similar examples:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28cis%28pi%2F4%29%29%29%5E4+=+%282%5E4%29%28cis%284%2A%28pi%2F4%29%29%29+=+16%28cis%28pi%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%28cis%28pi%2F12%29%29%29%5E8+=+%281%5E8%29%28cis%288%2A%28pi%2F12%29%29%29+=+cis%282pi%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );