Suppose $B$ is a bounded region in complex plane. In complex plane, one usually deals with complex moments, i.e. $\int_B {z}dxdy$ where $z \in \mathbb{C}$. What is so special about this complex moment compared to the real moments, i.e $\int_B {x^my^n}dxdy$ where $m,n \in \mathbb{N}$? I don see the reason using complex moments instead of real moments.