Alright, i goes in a pattern yes?

i

^{0}= 1

i

^{1}= i

i

^{2}= -1

i

^{3}= -i

i

^{4}= 1

And so on.

Now for the question

I see a lot that the reason i

^{4}= 1 is as follows. (i

^{3})(i

^{1}) = i

^{4}

Simple enough, however when they go into further detail questions arise for me. (i

^{3})(i

^{1}) = (-i)(i)

This makes sense because i

^{3}as we stated above is equal to -i, and i

^{1}is just i. So logically I look at this and thought "How can positive one come from this?" It would have to be -i or -1. The only way I can see it work is if you broke i

^{4}into two i

^{2}s, therefore giving you two -1s and giving you +1. Funny enough a video I watched explaining imaginary numbers sort of did this.

The person in the video says that -i is the same as -1, and what is -1 well that is equal to i

^{2}. So if we go along with what he says, is it safe to just look at i as 1 and -1?