document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207569>Question 1207569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Finding the Principal Root of a Complex Number<BR>\n" );
document.write( "   (-8i)^(1/3)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845515 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=845515\">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=%28-8i%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28-8i%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Write the given complex number in cis(theta) form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288cis%28270%29%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%288cis%28270%29%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use deMoivre's Theorem to find the principal root:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%288%5E%281%2F3%29%29%28cis%28270%2F3%29%29%29=2cis%2890%29 ALIGN=MIDDLE  ALT=\"%28%288%5E%281%2F3%29%29%28cis%28270%2F3%29%29%29=2cis%2890%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Convert the result back to a+bi form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%2Bi%29=2i ALIGN=MIDDLE  ALT=\"2%280%2Bi%29=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 2i<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%5E3=8i%5E3=8%28-i%29=-8i ALIGN=MIDDLE  ALT=\"%282i%29%5E3=8i%5E3=8%28-i%29=-8i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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