Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
geramul
Posts: 11
Joined: Wed Oct 24, 2012 9:52 am
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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
Posts: 197
Joined: Sun Feb 22, 2009 10:05 pm
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### Re: Question about imaginary numbers

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
Posts: 11
Joined: Wed Oct 24, 2012 9:52 am
Contact:

### Re: Question about imaginary numbers

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