How do you simplify i^279i279?

1 Answer
BeeFree
Jan 14, 2016

An easy trick is to simply divide 279 by 4 and use the remainder to find your answer ...

Explanation:

Exponential powers of imaginary number ii cycle through only 4 possible results :

i^1=ii1=i
i^2=-1i2=−1
i^3=-ii3=−i
i^4=1i4=1

i^5=ii5=i, etc...

Now, divide the exponent by 4 and find the remainder .

For example, i^6i6: 6/4=164=1 Remainder 22
Next, simply look up the value of i^2i2 which is -1−1
So, i^6=-1i6=−1

i^279: 279/4=69 " with a Remainder"=3i279:2794=69 with a Remainder=3

i^279=i^3=-ii279=i3=−i

hope that helped

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