Imaginary numbers?

Question

I just need the values of the following.

1. i^-20
2. i^-25
3. i^-30
4. i^-102

These will help me with my homework. I need to understand how i reacts with different exponents.

Answer 1

Every time you multiply by 'i', you rotate 90 degrees anti-clockwise on the number plane.

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

And then it just repeats.

Answer 2

I think this will help you see the pattern:
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
i^6 = -1
i^7 = -i
i^8 = 1
and so on.