Complex numbers in a frequency domain of a 2D image I am try to grasp the idea of frequency domain for images. I think get the basics, but now I've stuck with a question that I can't find appropriate answer anywhere.
How are frequency domain and complex numbers in relationship?
I've read this article from DSPguide and I understand that after applying DFT to an image in spatial domain, we get two planes: real and imaginary plane. By doing some calculations, we can get amplitude and phase planes. For what is the phase plane used for?
The real and imaginary plane are also the symmetric and anti-symmetric planes.  Image content that is symmetric around the center lines will show up in the real plane.  Image content that is opposite in brightness across the center lines will appear in the imaginary plane.  Data that is neither or some combination of both will end up in both, with the phase angle indicating the mix or a shift (or rotation wrapping around the edges) from symmetric to anti-symmetric.