Question 56164: How do you compute "i" to the 34th power?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! How do you compute "i" to the 34th power?
NOTE THE FOLLOWING
I^1=I......................................1
I^2=-1.........................................2
I^3 = (I^2)*I=-I..................................3
I^4=(I^2)*(I^2)=(-1)*(-1)=1............................4
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YOU WILL FIND THE ROCESS REPEATS IT SELF NOW
I^5=(I^4)*I=I^1
I^6=(I^4)(I^2)=I^2
I^7=(I^4)(I^3)=I^3
I^8=(I^4)(I^4)
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SO WE NEED TO NOTE ONLY THE FIRST 4 EQNS.
THEY CAN BE SUMMARISED IN TO ONE RULE...
DIVIDE THE POWER OF I WITH 4.IF THE REMAINDER IS
A)0 THEN ANSWER IS +1
B)1 THEN ANSWER IS I
C)2 THEN ANSWER IS -1
D)3 THEN ANSWER IS -I
IN YOUR EXAMPLE POWER OF I IS 34..DIVIDING WITH 4 ..THE REMAINDER IS 2
HENCE ANSWER IS -1
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