Question

How do you simplify `i^123458`?

Answer 1

Factor out `i^4`

Explanation:

The nice thing about powers of "i" is that there are only four possible answers: i, -i, 1, and -1.
Since `i=sqrt(-1)` then `i^4=(i^2)^2=1`. "i" to a power of any multiple of four ( `i^4,i^8,i^16,...)` is 1 , so factor out i to the power that is the next lower multiple of four, in this case 123456.

`i^123458=i^123456*i^2=1*i^2=(sqrt(-1))^2=-1`