document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280701>Question 280701</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find (sqrt3 + i) using DeMoivre's Theorem?<BR>\n" );
document.write( "Leave answer in a polar form. Show work! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204450 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=204450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> DeMoivre's Theorem is usually used to raise complex numbers to a power. So I suspect that you left out an exponent. If so and if you are still not able to figure out the problem after reading what follows, please repost your question.<br><BR>\n" );
document.write( "(Note: For unknown reasons Algebra.com's formula software does not handle notation for inverse functions well. So I will use \"acos\" in place of cos^-1 and asin for sin^-1 in the expressions below.)<BR>\n" );
document.write( "If all you have to do is rewrite the complex number in polar form then the formula is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+bi+=+sqrt%28a%5E2+%2B+b%5E2%29%28cos%28acos%28a%2F%28sqrt%28a%5E2+%2B+b%5E2%29%29%29%29+%2B+i%2Asin%28asin%28b%2F%28sqrt%28a%5E2+%2B+b%5E2%29%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using this on your complex number we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29+%2B+1i+=+sqrt%28%28sqrt%283%29%29%5E2+%2B+1%5E2%29%28cos%28acos%28sqrt%283%29%2Fsqrt%28%28sqrt%283%29%29%5E2+%2B+1%5E2%29%29%29%29+%2B+i%2Asin%28asin%281%2Fsqrt%28%28sqrt%283%29%29%5E2+%2B+1%5E2%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2B1%29%28cos%28acos%28sqrt%283%29%2Fsqrt%283%2B1%29%29%29+%2B+i%2Asin%28asin%281%2Fsqrt%283%2B1%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%28cos%28acos%28sqrt%283%29%2Fsqrt%284%29%29%29+%2B+i%2Asin%28asin%281%2Fsqrt%284%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28cos%28acos%28sqrt%283%29%2F2%29%29+%2B+i%2Asin%28asin%281%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"2%28cos%28acos%28sqrt%283%29%2F2%29%29+%2B+i%2Asin%28asin%281%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using degrees, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=acos%28sqrt%283%29%2F2%29+=+asin%281%2F2%29+=+30 ALIGN=MIDDLE  ALT=\"acos%28sqrt%283%29%2F2%29+=+asin%281%2F2%29+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (Use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F6 ALIGN=MIDDLE  ALT=\"pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > for radians.) We now have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28cos%2830%29+%2B+i%2Asin%2830%29%29 ALIGN=MIDDLE  ALT=\"2%28cos%2830%29+%2B+i%2Asin%2830%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "With polar form and DeMoivre's Theorem, it is very easy to raise complex numbers to powers. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );