Question

How do you simplify `i^64`?

Answer 1

I found: `i^64=1`

Explanation:

I know that:
`i^1=sqrt(-1)=i`
`i^2=(sqrt(-1))^2=-1`
`i^3=i*i^2=i*-1=-i`
`i^4=i^2*i^2=-1*-1=1`
`i^5=i*i^2*i^2=i*(-1)*(-1)=i` AGAIN
`i^6=i^2*i^2*i^2=(-1)(-1)(-1)=-1`
now it repeats the same pattern: `i,-1,-i,1` every 4.

You have `i^64=(i^8)^2=(i^4*i^4)^2=(1*1)^2=1`