How do you simplify #i^279#?

Question

1604 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-14T01:14:32

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

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

#i^1=i#
#i^2=-1#
#i^3=-i#
#i^4=1#

#i^5=i#, etc...

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

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

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

#i^279=i^3=-i#

hope that helped