document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583804>Question 583804</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you expand this complex number in a standard complex number format? <BR>\n" );
document.write( "(1/2-1/2i)^4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372609 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=372609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Instead of calculating (1/2-(1/2)i)^4, I'm going to calculate 4*(1/2-(1/2)i)^4 \r<BR>\n" );
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document.write( "4*(1/2-(1/2)i)^4\r<BR>\n" );
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document.write( "(sqrt(2))^4*(1/2-(1/2)i)^4\r<BR>\n" );
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document.write( "(sqrt(2)*(1/2-(1/2)i))^4\r<BR>\n" );
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document.write( "(sqrt(2)/2-(sqrt(2)/2)i))^4\r<BR>\n" );
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document.write( "(cos(pi/4)-i*sin(pi/4))^4\r<BR>\n" );
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document.write( "cos(4*pi/4)-i*sin(4*pi/4)\r<BR>\n" );
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document.write( "cos(pi)-i*sin(pi)\r<BR>\n" );
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document.write( "-1-i*(0)\r<BR>\n" );
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document.write( "-1\r<BR>\n" );
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document.write( "So 4*(1/2-(1/2)i)^4 = -1. \r<BR>\n" );
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document.write( "But we really want to know the value of (1/2-(1/2)i)^4\r<BR>\n" );
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document.write( "So all we need to do is divide both sides by 4 to get \r<BR>\n" );
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document.write( "(1/2-(1/2)i)^4 = -1/4\r<BR>\n" );
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document.write( "So the final answer is <a  rel=nofollow HREF=\"http://www.codecogs.com/eqnedit.php?latex=\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}\" target=\"_blank\"><IMG STYLE=\"max-width:80%;\" src=\"http://latex.codecogs.com/gif.latex?\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}\" title=\"\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}\" /></a> </SPAN>\n" );
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