To show that reduction of Fourier transform of $\frac{1}{x+iy}$ is $\frac{-2\pi i}{\omega_{x}+i\omega_{y}}$

Question

Can someone tell me the reduction that the Fourier transform of $\frac{1}{x+iy}$ is $\frac{-2\pi i}{\omega_{x}+i\omega_{y}}$. I have tried rewriting $\frac{1}{x+iy}$ as $\frac{1}{x}(\sum_{k=0}^{\infty}(\frac{-iy}{x})_{k})$, but it is not a convergent sequence.