document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=781799>Question 781799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "I am stuck! I am to find all the solutions in the complex number set of Z^5=-32\r<BR>\n" );
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document.write( "It has a real solution of -2 but also has 4 complex solutions.\r<BR>\n" );
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document.write( "so using the euler equation I came up with \r<BR>\n" );
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document.write( "z= |z|cos5&#952; + isin5&#952;\r<BR>\n" );
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document.write( "so -2 = 2 cos5&#952; + isin5&#952;\r<BR>\n" );
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document.write( "I'm not sure how to get the solutions from this equation. I know it's easy to see if graphed, but I cannot figure out where to start. \r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #476112 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=476112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It has a real solution of -2 but also has 4 complex solutions.\r<BR>\n" );
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document.write( "so using the euler equation I came up with \r<BR>\n" );
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document.write( "z= |z|cos5&#952; + isin5&#952;\r<BR>\n" );
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document.write( "so -2 = 2 cos5&#952; + isin5&#952;<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "z^5 + 32 --> 32cis(t), t = 0 + n*360, n = 0,1,2,3,4\r<BR>\n" );
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document.write( "Zeroes at 2cis(t/5)<BR>\n" );
document.write( "--> 2, 2cis(72), 2cis(144), 2cis(216), 2cis(288)<BR>\n" );
document.write( " </SPAN>\n" );
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