document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=631743>Question 631743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please use de Moivre’s Theorem to find [2-2 sqrt (3i)^10].  Write your answer in exact rectangular form. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #397777 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=397777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [2-2 sqrt (3i)]^10.  Write your answer in exact rectangular form.<BR>\n" );
document.write( "If you mean [2 - 2sqrt(3)i]^10<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "r = sqrt(4 + 12) = 4<BR>\n" );
document.write( "tan = -sqrt(3) --> angle = 300 degs<BR>\n" );
document.write( "--> 4cis(300)<BR>\n" );
document.write( "^10 --> 4^10cis(3000)<BR>\n" );
document.write( "= 2^20cis120<BR>\n" );
document.write( "= 2^20*(-0.5 + i*sqrt(3)/2)<BR>\n" );
document.write( "= 2*19*(-1 + isqrt(3))<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "or <BR>\n" );
document.write( "-524288 + i*524288*sqrt(3)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );