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The concurrent complementary operators method (C-COM) has recently been applied to time-harmonic solution of Maxwell equations in two-dimensional space. In this paper, we present the application of the C-COM to the problem of electromagnetic scattering by conducting cylindrical objects in two-dimensional spaces. We show that the C-COM can effectively annihilate surface waves that impinge on the boundary at or near grazing incidence. The effectiveness of the C-COM is due to the fact that its wave absorption mechanism is independent of the wave number. To demonstrate the effectiveness and robustness of the C-COM in time-harmonic simulation, we present several numerical experiments. A strong agreement is obtained between the C-COM solution and the reference solutions even when the computational boundary is positioned only a fraction of a wavelength from the scatterer's body. Furthermore, we present a numerical experiment that shows the behavior of C-COM when waves impinge on the outer boundary at oblique incidence.