What’s the best way to remember the powers of “i” (imaginary numbers)?

bigboy105us: What’s the best way to remember the powers of “i” (imaginary numbers)?
I do have a table that has i^1 to i^12 but what if I need to find out how to simplify with a larger exponent than 12 or further than that? What’s the best way to remember the powers of “i”? I know sometimes the answer is 1, -1, i or -i. But I’m not sure how to tell which one of those.

Answers and Views:

Answer by soccerguy
just remember it by multiples

for example i^4 will be the same as i^8 and i^12 and i^16 because all those are multiple of 4

Answer by Anon
One way to find the result of say, i^1033 for example, would be to see how many times 4 divides into it and use the remainder as the exponent of i. You can easily recall that i^4 = 1, so in the above example you would have 258 (i^4)’s multiplied together, giving i^1032, which is just 1. Since the remainder on division is 1, the answer is just i^1 or i.

Answer by aBitRusty
you just need 4 , or 3 , and dont need to remember them, those are just easily derived

i^1 = .. yes. i
i^2 = – 1 (because it’s defined that way)
i^3 = i^2 * i = -1 * i = -i
i^4 = (i^2)^2 = (-1)^2 = 1

anything else.. i^23, -i^34, has nothing to do with memorizing
you can just use the basic first 2 to quickly figure it out

i^23 = i^(11*2 + 1) = i^(11*2) * i = (-1)^11 * i = -i