document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178763>Question 1178763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> finding the nth root of a complex number<BR>\n" );
document.write( " (16i)^1/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808203 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=808203\">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=16i+=+0%2B16i+=+16cis%28pi%2F2%29 ALIGN=MIDDLE  ALT=\"16i+=+0%2B16i+=+16cis%28pi%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use deMoivre's Theorem on the last form to find the 4th roots<br><BR>\n" );
document.write( "(1) Find the \"primary\" root.  To find the nth root of a number in a*cis(theta) form, take the nth root of a, and divide the angle theta by n.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816cis%28pi%2F2%29%29%5E%281%2F4%29+=+%2816%5E%281%2F4%29%29%2Acis%28pi%2F8%29+=+2%2Acis%28pi%2F8%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Find the other roots.  The n n-th roots of a number all have the same magnitude, and they are distributed around the complex plane in intervals of (2pi)/n.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F4+=+pi%2F2 ALIGN=MIDDLE  ALT=\"2pi%2F4+=+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The 4th roots are at intervals of pi/2 in the complex plane.  Starting with the \"primary\" root of 2*cis(pi/8), the four 4th roots of 16i are<br><BR>\n" );
document.write( "2cis(pi/8)<BR>\n" );
document.write( "2cis(5pi/8)<BR>\n" );
document.write( "2cis(9pi/8)<BR>\n" );
document.write( "2cis(13pi/8)<br><BR>\n" );
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