Question

Simplify.
i^67

Answer 1

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

i^5 = i

This pattern repeats indefinitely.

So if you want to find i^k where k is any number, you just divide k by 4 and determine the remainder.

So if k = 25 for example, then

25/4 = 6 remainder 1

The remainder will tell us the value of i^25. Since the remainder is 1, this means that i^25 = i^1, but from above, i^1 = i, this means that

i^25 = i

Answer 2

So what you need to do is divide 67 by 4 to find the remainder

Once you have the remainder, use it to figure out what i^67 is