Answer:
We can use a trick here. Let's look at the first few exponents of i to realize this:
i^0 = 1
i^1 = i
i^2= -1
i^3 = -i
i^4 = 1
i^5 = i
i^6 = -1
i^7 = -i
we can see that the pattern (1, i, -1, -i) repeats. Since 82/2 = 41, and 41 is only divisible by 1, i^41 = i, and i^2 = -1. -1*i = -i, so i^82 = -i.
Step-by-step explanation:
