e^-it as t approaches infinity

Question

How do I evaluate $$ \lim_{t\rightarrow \infty } e^{-it}$$

I feel like it should be 0, but I'm not sure if the $i$ changes things.

Answer 1

Hint:

$$e^{iat}=\cos at + i \sin at$$

Answer 2

Here is how you can interpret this limit using argand plane. The solution region is a square and there is no definite value for this limit

Answer 3

$e^{it}=(-1)^{n}$ when $t=n\pi$ so the limit does not exist.