document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33940>Question 33940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, need help with simplifying complex number <BR>\n" );
document.write( "i^51, have no idea how to do it, if you can explain it please i will appreciate it </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20326 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=20326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> powers of \"i\" go thru a cycle; i, i^2=-1, i^3=-i, i^4=1<BR>\n" );
document.write( "So, divide 51 by 4 to get 12 with a remainder of 3<BR>\n" );
document.write( "Then i^51=[(i^4)^(12)](i^3)= [(1^12)][-i]= -i<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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