Does e^(-infinity + i*w*infinity) equal 0 or 1?

[gomes.]

Does e^[(-infinity)+(i*w*infinity)] = 0 or 1?

w = omega

 

[hgfalling]

Well, it's not really quite correct to write that $e^{-\infty+i\omega\infty}$ EQUALS something. But I think you are asking: $$\lim_{x\rightarrow\infty} e^{-x+i\omega x} = \lim_{x\rightarrow\infty} e^{-x} e^{i\omega x}$$

Now this last expression has $e^{-x} \rightarrow 0$ and the imaginary power of $e$ is bounded, so the entire expression goes to 0.

 

[gomes.]

thanks! got it now