document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426015>Question 426015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am taking a placement test next week and i need some help with some math.\r<BR>\n" );
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document.write( "with complex numbers i^32 power </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296453 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each time you multiply a number by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you<BR>\n" );
document.write( "rotate 90 degrees in the complex plane.<BR>\n" );
document.write( "You start at <BR>\n" );
document.write( "i^0 = 0 degrees = (+) real numbers<BR>\n" );
document.write( "i^1 = 90 degrees = (+) imaginary<BR>\n" );
document.write( "i^2 = 180 degrees = (-) reals<BR>\n" );
document.write( "i^3 = 270 degrees = (-) imaginary<BR>\n" );
document.write( "i^4 = 360 degrees = back to (+) reals<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+i%5E4 ALIGN=MIDDLE  ALT=\"+i%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a complete rotation back to<BR>\n" );
document.write( "0 degrees<BR>\n" );
document.write( "Divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2F4+=+8 ALIGN=MIDDLE  ALT=\"32%2F4+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is 8 times around back to 0 degrees with no remainder,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+i%5E32+=+1+ ALIGN=MIDDLE  ALT=\"+i%5E32+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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