Real number that tends to negative infinity multiplied by complex number

Question

I was trying to find the Fourier transform of $x(t) = e^{−a|t|}, a>0$ and came across this limit: $$\lim_{x\to-\infty} e^{(\alpha-\omega\cdot\jmath)\cdot t}, \jmath\in\mathbb{C}$$ In the answer of the question, this was equal to $0$ but I don't understand why. The limit in the exponent is $-\infty$ for this to be true, but what is the meaning of $-\infty$ in the complex plane?

Answer 1

This is answered on this post.

By splitting up the exponents, since the exponent with the complex number is bounded, it doesn't affect the multiplication with zero.