document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221204>Question 221204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify imaginary i^33<BR>\n" );
document.write( "as much as possible<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165982 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10553)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=165982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> simplify imaginary i^33 as much as possible\r<BR>\n" );
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document.write( "When calculating large powers of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i ALIGN=MIDDLE  ALT=\"i\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we simply need to divide the exponent by 4, and the remainder is our answer. That is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E33 ALIGN=MIDDLE  ALT=\"i%5E33\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E%2833%2F4%29 ALIGN=MIDDLE  ALT=\"i%5E%2833%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E8 ALIGN=MIDDLE  ALT=\"i%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E1 ALIGN=MIDDLE  ALT=\"i%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. As mentioned before, this remainder <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E1 ALIGN=MIDDLE  ALT=\"i%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be the answer, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28i%29 ALIGN=MIDDLE  ALT=\"highlight_green%28i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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