I'm not sure I understand how to calculate Fourier transforms. How do I deal with the $i$ in the following?
Let $$f(x) = e^{ cx} - e^{(c+1)x}, \ \ c > 0$$
for $x < 0$ (and $f(x) = 0$ otherwise).
My book states the Fourier transform $\hat{f}(\xi)$ is
$$ \hat{f}(\xi) = -\frac{1}{(\xi - ic)(\xi - i(c+1))}$$
and I have no idea how it computes this?
How do you calculate $$ \int_{-\infty}^0 f(x) e^{i\xi x}dx$$
and get the same answer as above?