document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115817>Question 115817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> change -sqrt3 + i in trigonometric form and find\r<BR>\n" );
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document.write( "1. (-sqrt3+i)^5, answer in rectangular form such as a+bi?\r<BR>\n" );
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document.write( "2. (-sqrt3 + i)^1/3, write all answers separately in trigonometric form using degree angles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84269 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=84269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> change -sqrt3 + i in trigonometric form and find <BR>\n" );
document.write( "1. (-sqrt3+i)^5, answer in rectangular form such as a+bi?<BR>\n" );
document.write( "r = sqrt[(-sqrt3)^2 + 1^2] = sqrt[4] = 2<BR>\n" );
document.write( "theta = tan^-1[1/(-srt3)] = 150 degrees<BR>\n" );
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document.write( "Therefore: (-sqrt3+i) = [2cis(150)]^5<BR>\n" );
document.write( "= 32cis(5*150)<BR>\n" );
document.write( "= 32 cis (750)<BR>\n" );
document.write( "= 32cis(30)<BR>\n" );
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document.write( " <BR>\n" );
document.write( "2. (-sqrt3 + i)^1/3, write all answers separately in trigonometric form using degree angles?<BR>\n" );
document.write( "(-sqrt3 + i)^(1/3) = [2cis(150)]^(1/3) <BR>\n" );
document.write( "= 2^(1/3)cis((1/3)150)<BR>\n" );
document.write( "=2^(1/3)cis(50)<BR>\n" );
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document.write( "I'm assuming you want the principal root, not all three cube roots<BR>\n" );
document.write( "If you want all three roots you need to use (1/3)[150+360k) where <BR>\n" );
document.write( "k = 0, then k=1, then k=2<BR>\n" );
document.write( "You would have angles of 50, 50+120, and 50+240<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan<BR>\n" );
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