I know that complex exponentials are eigen functions of LTI systems for example e^{j2t}, e^{-j5t} , e^{j8t} .

If we can define complex exponential as e^{st} where s is a complex number. Can we say that e^t,e^{2t},e^{(2-j4)t} are still complex exponentials and they are eigenfunctions to LTI systems ?

I know that complex number includes real numbers and 1 , 2 and 2-j4 are indeed complex numbers. What I'm curious about is , when 2 or 2-j4 is exponent i.e. e^{2t},e^{(2-j4)t} are eigenfunctions to LTI systems?

Thanks for be interested.