I am trying to solve the following definite integral.
$$\int_{-\infty}^0 e^{\omega (i(x - z) + |a - y|)} d \omega + \int_{0}^\infty e^{\omega (i(x - z) - |a - y|)} d\omega$$
where $i$ is the imaginary number, $a, x, y, z$ are constants.
I get that it's equal to
$$ \frac{2|a - y|}{(a - y)^2 + (x - z)^2}.$$
Is this correct?