Scattering of the two dimensional electromagnetic waves is studied by the infinite sequences of zeros arising on the complex plane, which just correspond to the null points of the far field pattern given as a function of the azimuthal angle θ. The convergent sequences of zeros around the point of infinity are evaluated when the scattering objects are assumed to be N-polygonal cylinders. Every edge condition can be satisfied if the locations of zeros are determined appropriately. The parameters, which allow us to calculate the exact positions of zeros, are given by the asymptotic analysis. It is also shown that there are N-directions of convergence, which tend to infinity. An illustrative example is presented.