document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116764>Question 1116764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you final all complex solutions and write all answers in both trigonometric and rectangular form?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-8=0 ALIGN=MIDDLE  ALT=\"x%5E3-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731686 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=731686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Put the numbers in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28ix%29 ALIGN=MIDDLE  ALT=\"e%5E%28ix%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > format and use deMoivre's Theorem.<br><BR>\n" );
document.write( "deMoivre's Theorem says that to find the n-th root of a complex number, you take the n-th root of the modulus and divide the angle by n.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29%2Bi%2Asin%28x%29+=+cis%28x%29+=+e%5E%28ix%29 ALIGN=MIDDLE  ALT=\"cos%28x%29%2Bi%2Asin%28x%29+=+cis%28x%29+=+e%5E%28ix%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For your problem, we are to find the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"8%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+8e%5E%28i%2A0%29+=+8e%5E%28i%2A2pi%29+=+8e%5E%28i%2A4pi%29%7D%7D%3Cbr%3E%0D%0AThen%3Cbr%3E%0D%0A%7B%7B%7B8%5E%281%2F3%29+=+%288%29%5E%281%2F3%29%2Ae%5E%28i%2A0%2F3%29+=+%288%29%5E%281%2F3%29%2Ae%5E%28i%2A2pi%2F3%29+=+%288%29%5E%281%2F3%29%2Ae%5E%28i%2A4pi%2F3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The three cube roots of 8 are<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5Ei%280%29+=+2cis%280%29+=+2 ALIGN=MIDDLE  ALT=\"2e%5Ei%280%29+=+2cis%280%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5E%28i%282pi%2F3%29%29+=+2cis%282pi%2F3%29+=+-1%2F2%2Bi%2Asqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"2e%5E%28i%282pi%2F3%29%29+=+2cis%282pi%2F3%29+=+-1%2F2%2Bi%2Asqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5E%28i%284pi%2F3%29%29+=+2cis%284pi%2F3%29+=+-1%2F2-i%2Asqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"2e%5E%28i%284pi%2F3%29%29+=+2cis%284pi%2F3%29+=+-1%2F2-i%2Asqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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