I would like to know how to calculate the the Fourier transform of the function $S:\mathbb{R^2}/\{0\}\to\mathbb{R^2}$ given by
$$S(x_1,x_2)=\frac{(x_2,-x_1)}{x_1^2+x_2^2}$$
in the book I was reading, the author only says that
$$\hat{S}(\zeta_1,\zeta_2)=C\frac{(\zeta_2,-\zeta_1)}{\zeta_1^2+\zeta_2^2}$$ where $C$ is a constant.
And I not used to calculate the transform of a two variables function.
any hint would be really apreciated!