Question about imaginary numbers

[geramul]

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?

[buddy]

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.

why? (-i)*(i) = -1*i*i = -1*(i^2) = -1*-1 = +1

The person in the video says that -i is the same as -1

thats wrong. -1 = i*i = 1*i*i but -i = -1*i = i*i*i and 1 =/= i

[geramul]

I think I get it now, thanks. I get stuck on the stupidest stuff sometimes :P.