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## #1 2006-05-10 01:48:18

MATHSKITZO
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### i

Can someone explain exactly why and how this is true?

i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i

Thank you.

'Math is not a means to arrive at truth, Math IS the only truth!'

## #2 2006-05-10 03:07:39

Ricky
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### Re: i

Start out at i^1, which of course is just i.  Now what's i^2?  Well, another way to write (i)^2?  We know i is √-1, so i^2 is (√-1)^2, which of course is just -1.

Continue this pattern.  What's i*-1?  i*i*-1?  And so on...

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

## #3 2006-05-10 05:13:48

MATHSKITZO
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### Re: i

Ohhhhh, I see it now, I was thinking illogically about the fourth power.   I should have wrote it down and thought about it.

Thanks.

'Math is not a means to arrive at truth, Math IS the only truth!'