SOLUTION: How do I evaluate the power of i in i ^97 and i^-34? Please give an explanation. Thanks.

Question 40931: How do I evaluate the power of i in i ^97 and i^-34? Please give an explanation. Thanks.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
How do I evaluate the power of i in i ^97 and i^-34? Please give an explanation. Thanks.
SEE THE PATTERN IN POWERS OF I
1.I^1=I
2.I^2=-1
3.I^3=I^2*I=-I
4.I^4=(I^2)^2=1
---------------------------------------------
5.I^5=I^4*I=I
6.I^6=I^4*I^2=I^2=-1
7.I^7=I^4*I^3=I^3=-I
8.I^8=I^4*I^4=I^4=1
--------------------------------------
SO THE ANSWERS REPEAT WITH EVERY 4TH.POWER....SO WE CONCLUDE
I=I^1=I^5=I^9=.........=I^(4N+1)
-1=I^2=I^6=I^10........=I^(4N+2)
-I=I^3=I^7=I^11........=I^(4N+3)
1=I^4=I^8=I^12=........=I^4N
-----------------------------------------------------------
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
I^97=I^(4*24+1)=I
FOR -34...WE GET -34=4*-9+2...SO....
I^-34=I^(-4*9+2)=I^2=-1
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