document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=459752>Question 459752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I simplify each expression? 1. i^7     2.  i^32   and write the definition for i = and i^2 =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315269 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=315269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do I simplify each expression? 1. i^7 2. i^32 and write the definition for i = and i^2 = <BR>\n" );
document.write( "---<BR>\n" );
document.write( "sqrt(-1) = i<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( "Then the cycle repeats over and over again.<BR>\n" );
document.write( "------<BR>\n" );
document.write( "So i^7 = i^(4+3) = i^4*i^3 = 1*i^3 =  = -i<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "i^32 = i(4*8) = (i^4)^8 = 1^8 = 1<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );