Consider two Gaussian integers a and b. a=x+iy and b=c+id in the Cartesian plane. Any C=ab then C is the linear combination of (x+iy)and (−y+ix) similarly it is also a linear combination of (c+id) and (−d+ic). In general one can tell that C falls on the grid created by vector 'a' and 'ia' in Cartesian plane. Any Gaussian integer has a number of residues equal to its norm; it can be easily proved by the graphical method. Caley tables of that Gaussian prime number and its norms are equivalent. hint: prove it also by graphical method.