document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121401>Question 121401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the first 10 powers of i. Observe the pattern. Explain how to quickly calculate any whole number power of i.( ex. What is i^312?)<BR>\n" );
document.write( "I know how to calculate the first ten powers and I see the pattern but I am awful at explaining to other people. Can you help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89075 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley71><B>checkley71(8403)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley71><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=89075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i^1=sqrt-1<BR>\n" );
document.write( "i^2=-1<BR>\n" );
document.write( "i^3=1sqrt-1<BR>\n" );
document.write( "i^4=1<BR>\n" );
document.write( "i^5=1sqrt-1<BR>\n" );
document.write( "i^6=-1<BR>\n" );
document.write( "i^7=-1sqrt-1<BR>\n" );
document.write( "i^8=1<BR>\n" );
document.write( "i^9=1sqrt-1<BR>\n" );
document.write( "i^10=-1<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "i^312=i^(78*4) or i^4=1<BR>\n" );
document.write( "IF THE POWER IS DIVISABLE BY 4 THEN THE ANSWER IS (1)<BR>\n" );
document.write( "IF DIVIDING THE POWER BY 4 GIVES A REMAINDER OF 1 THEN THE ANSWER IS (SQRT-1)<BR>\n" );
document.write( "IF DIVIDING THE POWER BY 4 GIVES A REMAINDER OF 2 THEN THE ANSWER IS (-1)<BR>\n" );
document.write( "IF DIVIDING THE POWER BY 4 GIVES A REMAINDER OF 3 THEN THE ANSWER IS (1SQRT-1) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );