Question about imaginary numbers  TOPIC_SOLVED

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Question about imaginary numbers

Postby geramul on Wed Nov 28, 2012 7:24 pm

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 :roll:

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?
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Re: Question about imaginary numbers  TOPIC_SOLVED

Postby buddy on Wed Nov 28, 2012 9:02 pm

geramul wrote: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

geramul wrote: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
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Re: Question about imaginary numbers

Postby geramul on Wed Nov 28, 2012 10:58 pm

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