document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998754>Question 998754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find : z=(1-i)^23 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616506 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=616506\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find : z=(1-i)^23 <BR>\n" );
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document.write( "Use DeMoivre<BR>\n" );
document.write( "Note: 1-i is in QIV<BR>\n" );
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document.write( "r = sqrt(1^2+1^2) = sqrt(2)<BR>\n" );
document.write( "theta = arctan(-1/1) = arctan(-1) = 315 degrees or (7/4)pi<BR>\n" );
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document.write( "(1-i)^23 = (sqrt(2))^23*cis(23(7/4)pi)<BR>\n" );
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document.write( "= 2896.31*cis(40.25pi) = 2896.31*cis(pi/8)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "= 2896.31*cos(pi/8) + 2896.31*sin(pi/8)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "stan H.<BR>\n" );
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