Raising i to a large power on a Ti-83

Question

When I input this on my graphing calculator I get the correct answer:

i^4
1

However when I do this with larger numbers I get a weird answer

i^64
1-3.6E^-12i

Despite the fact that the answer to i^64 is also 1. Why does the calculator start to have problems with large powers of i?

Answer 1

floating point errors... its simply because the calculator is using a general algorithm to solve this, and the calculator has to round a little to store the bits in memory, so the result is a little off. Of course, the calculator is only $0.0000000000036$ off; not bad. When you encounter this it is pretty safe to drop the extra part.