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How do I evaluate the power of i in i ^97 and i^-34? Please give an explanation. Thanks.
\n" ); document.write( "SEE THE PATTERN IN POWERS OF I
\n" ); document.write( "1.I^1=I
\n" ); document.write( "2.I^2=-1
\n" ); document.write( "3.I^3=I^2*I=-I
\n" ); document.write( "4.I^4=(I^2)^2=1
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "5.I^5=I^4*I=I
\n" ); document.write( "6.I^6=I^4*I^2=I^2=-1
\n" ); document.write( "7.I^7=I^4*I^3=I^3=-I
\n" ); document.write( "8.I^8=I^4*I^4=I^4=1
\n" ); document.write( "--------------------------------------
\n" ); document.write( "SO THE ANSWERS REPEAT WITH EVERY 4TH.POWER....SO WE CONCLUDE
\n" ); document.write( "I=I^1=I^5=I^9=.........=I^(4N+1)
\n" ); document.write( "-1=I^2=I^6=I^10........=I^(4N+2)
\n" ); document.write( "-I=I^3=I^7=I^11........=I^(4N+3)
\n" ); document.write( "1=I^4=I^8=I^12=........=I^4N
\n" ); document.write( "-----------------------------------------------------------
\n" ); document.write( "SO WRITE THE POWER OF I AS 4N+X...BY DIVIDING IT WITH 4 ..SAY FOR I^97...DIVIDE 97 WITH 4 TO GET 97=4*24+1...SO
\n" ); document.write( "I^97=I^(4*24+1)=I
\n" ); document.write( "FOR -34...WE GET -34=4*-9+2...SO....
\n" ); document.write( "I^-34=I^(-4*9+2)=I^2=-1 \n" ); document.write( "