This study introduces an alternative approach to the numerical solution of two-dimensional (2D) electromagnetic scattering problems by a numerical method of moments (MoM). The real source position vector is replaced by a complex quantity, then Green's function generates a complex source point beam, therefore the interactions between the far zone elements in the impedance matrix are neglected, except the basis functions near to the edges, strongly localizing the impedance matrix. The memory storage increases with the number of edges, but for a fixed number of the edges, it is linearly proportional with N, i.e. O(N). Consequently, the overall running time can be drastically reduced and the far zone scattering pattern and the near field can be found. The proposed procedure is first explained for the single perfectly electrically conducting (PEC) strip geometry, then extended to the scattering by 2D PEC objects with closed polygonal cross-sections. Numerical results are presented for a strip and a square cylinder in both polarizations. The relative errors are also compared with the standard MoM.