Hello Everyone!

I'm being reluctant when finding integrals involving complex exponentials, of the form:

1. $\displaystyle \int^{+\infty}_{-\infty}e^{-iat}dt$

2. $\displaystyle \int^{+\infty}_{0}e^{-iat}dt$

This is because I do not know what to do with infinities multiplied by a complex number, but I know as $\displaystyle t \rightarrow \infty$

Is there a way to solve this without getting into Fourier transform? I know that generalized functions are involved in those integrals, but can we got an answer without going through that?

Thanks!