document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=740092>Question 740092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having trouble with a question in my lesson. Could I have some help?\r<BR>\n" );
document.write( "\n" );
document.write( "(-1 + [SQRT(3)]i)^3 \r<BR>\n" );
document.write( "\n" );
document.write( "These are the options:\r<BR>\n" );
document.write( "\n" );
document.write( "A) 2 + 2[SQRT(3)]i <BR>\n" );
document.write( "B) -2 - 2[SQRT(3)]i <BR>\n" );
document.write( "C) 0 <BR>\n" );
document.write( "D) -8 <BR>\n" );
document.write( "E)  -8 + 8[SQRT(3)]i <BR>\n" );
document.write( "F)  8  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #451528 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=451528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2Bsqrt%283%29i%29%5E3 ALIGN=MIDDLE  ALT=\"%28-1%2Bsqrt%283%29i%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as you would calculate the cube of any binomial, using the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E3=a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E3=a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2Bsqrt%283%29i%29%5E3=%28-1%29%5E3%2B3%28-1%29%5E2sqrt%283%29i%2B3%28-1%29%28sqrt%283%29i%29%5E2%2B%28sqrt%283%29i%29%5E3=+-1%2B3sqrt%283%29i%2B3%28-1%29%28sqrt%283%29%29%5E2i%5E2%2B%28sqrt%283%29%29%5E3i%5E3=+-1%2Bsqrt%283%29i%2B3%28-1%29%283%29%28-1%29%2B%283sqrt%283%29%29%28-i%29=+-1%2B3sqrt%283%29i%2B9-3sqrt%283%29i=8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If you already learned about the polar form of complex numbers, you could transform the number into its polar form, if that made it easier for you.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Bsqrt%283%29i=2%28cos%28120%5Eo%29%2Bi%2Asin%28120%5Eo%29%29 ALIGN=MIDDLE  ALT=\"-1%2Bsqrt%283%29i=2%28cos%28120%5Eo%29%2Bi%2Asin%28120%5Eo%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has<BR>\n" );
document.write( "absolute value (or modulus): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2+=sqrt%28%28-1%29%5E2%2B%28sqrt%283%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"r=2+=sqrt%28%28-1%29%5E2%2B%28sqrt%283%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "argument: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=120%5Eo ALIGN=MIDDLE  ALT=\"theta=120%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplication and powers are easier in polar form.<BR>\n" );
document.write( "To multiply, you just multiply the absolute values and add the arguments.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28cos%28120%5Eo%29%2Bi%2Asin%28120%5Eo%29%29%29%5E3=2%5E3%28cos%283%2A120%5Eo%29%2Bi%2Asin%283%2A120%5Eo%29%29=8%28cos%28360%5Eo%29%2Bi%2Asin%28360%5Eo%29%29=8%281%2Bi%2A0%298%2A1=8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );