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