How do you simplify #i^752#?

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Answer 1 · 2016-01-24T23:53:21

#1#

Recall that #i=sqrt(-1)#. Because of this, #i^2=-1#. We can then use this fact to find #i^4#:

#i^2=-1#
#(i^2)^2=(-1)^2#
#i^4=1#

The fact that #i^4=1# is very useful. In fact, #i^752# can be expressed solely in terms of #i^4#.

Since #188xx4=752#, we can say that

#i^752=(i^4)^188#

And #i^4=1#, so

#i^724=1^188=1#