Determine the domain and range of the complex function:

$\displaystyle f(z)=e^{(x-y)\mathbf{i}}$

I know that forum wish that questions have worked associated with what one needs help with; however, my book doesn't help whatsoever in finding the domain and range. Therefore, I can't supply any work since I have no idea how do this problem. Can someone help me with solving this problem, thanks.