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**MATHSKITZO****Member**- Registered: 2006-05-08
- Posts: 21

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!'

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

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**MATHSKITZO****Member**- Registered: 2006-05-08
- Posts: 21

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!'

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