document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=392293>Question 392293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve/simplify\r<BR>\n" );
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document.write( "i to the 34th power?<BR>\n" );
document.write( "~thanks!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #278445 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=278445\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do you solve/simplify\r<BR>\n" );
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document.write( "i to the 34th power?<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The powers of i are cyclic.<BR>\n" );
document.write( "i = 1<BR>\n" );
document.write( "i^2 = -1<BR>\n" );
document.write( "i^3 = -i<BR>\n" );
document.write( "i^4 = 1<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "i^34 = i^32 * i^2<BR>\n" );
document.write( "= (i^4)^8 * i^2<BR>\n" );
document.write( "= 1^8 * i^2<BR>\n" );
document.write( "= i^2<BR>\n" );
document.write( "= -1<BR>\n" );
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document.write( "For i^n, divide n by 4 and keep the remainder<BR>\n" );
document.write( "= i^remainder<BR>\n" );
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