document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984794>Question 984794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the fifth roots of 32(cos 280° + i sin 280°). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605610 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i) Let z = 32(cos 280° + i sin 280°) = 32{cos(k*360° + 280°) + isin(k*360° + 280°)}, <BR>\n" );
document.write( "where k is an integer. \r<BR>\n" );
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document.write( "ii) ==> z^(1/5) = [32{cos(k*360° + 280°) + isin(k*360° + 280°)}]^(1/5) \r<BR>\n" );
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document.write( "==> z^(1/5) = 2[cos{(k*360° + 280°)/5} + isin{(k*360° + 280°)/5}] <BR>\n" );
document.write( "[Application of De-Moievere's theorem] \r<BR>\n" );
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document.write( "==> z^(1/5) = 2[cos(72k + 56) + isin(72k + 56)] \r<BR>\n" );
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document.write( "We can now get the 5 roots, by assigning k = 0, 1, 2, 3 & 4 \r<BR>\n" );
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document.write( "When k = 0, 1st root = 2(cos 56° + isin 56°) <BR>\n" );
document.write( "When k = 1, 2nd root = 2(cos 128° + isin 128°) <BR>\n" );
document.write( "When k = 2, 3rd root = 2(cos 200° + isin200°) <BR>\n" );
document.write( "When k = 3, 4th root = 2(cos 272° + isin 272°) <BR>\n" );
document.write( "When k = 4, 5th root = 2(cos 344° + isin344°) </SPAN>\n" );
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