document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030677>Question 1030677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the roots of (-1+sqrt 3i)^3/2 leaving the answer in polar from.<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 #645825 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the roots of (-1+sqrt 3i)^3/2 leaving the answer in polar from.<BR>\n" );
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document.write( "Polar form:: r(cos(t)+i*sin(t))<BR>\n" );
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document.write( "r = sqrt[1^2 + (sqrt(3))^2] = sqrt[4] = 2<BR>\n" );
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document.write( "t = arctan(sqrt(3)/(-1)] = arctan(-sqrt(3)) = (2/3)pi<BR>\n" );
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document.write( "Ans: r^(3/2)(cos[(2pi/3+2npi)/(3/2) + i*sin[(2pi/3+2npi)/(3/2)]<BR>\n" );
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document.write( "If n = 0, Ans = r^(3/2)[cos[(4/9)pi + i*sin[(4/9)pi]<BR>\n" );
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document.write( "If n = 1, Ans = r^(3/2)[cos[(4/9)pi+(4/3)pi] + isin[(4/9)pi + (4/3)pi]<BR>\n" );
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document.write( "= r^(3/2)*cis[(16/9)pi]<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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