Fourier transform of certain complex functions including conjugate

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For $y,a,t,s\in\mathbb{R},y\neq 0,t,s>1$, how can we compute the following integral? $$\int_{-\infty}^{+\infty}(x+iy)^{-s}(x-iy)^{-t}e^{2\pi i ax}dx$$