Ugh. This is a stupid question, but unfortunately it's impossible for me to let this go until I know the answer.
Alright, i goes in a pattern yes?
i0 = 1
i1 = i
i2 = -1
i3 = -i
i4 = 1
And so on.
Now for the question
I see a lot that the reason i4 = 1 is as follows. (i3)(i1) = i4
Simple enough, however when they go into further detail questions arise for me. (i3)(i1) = (-i)(i)
This makes sense because i3 as we stated above is equal to -i, and i1 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 i4 into two i2s, 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 i2. So if we go along with what he says, is it safe to just look at i as 1 and -1?