POWER OF PURE IMAGINARY NUMBERS: application exercise

The power of imaginary numbers is calculated using the following rules:
General rules
1. i^2 = -1
2. i^3 = -i
3. i^4 = 1
4. i^n = (i^4)^k * i^r, where n = 4k + r and 0 ≤ r < 4
Examples
1. i^5 = (i^4)^1 * i^1 = 1 * i = i
2. i^6 = (i^4)^1 * i^2 = 1 * (-1) = -1
3. i^7 = (i^4)^1 * i^3 = 1 * (-i) = -i
4. i^8 = (i^4)^2 = 1
Powers of imaginary numbers