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The far field of a two-dimensional beam resulting from an electric line source at a complex position is described, its half-power beamwidth determined, and its validity as an antenna beam indicated. Farfield diffraction by a half-plane is then determined from an exact uniform solution for an isotropic line source by making the source position complex. The same basic solution and technique are used for beam diffraction by a wide slit, with first-order interaction between the slit edges included. Numerical results for normal incidence illustrate the evolution of the diffraction patterns from those for an omnidirectional source to those for a highly directive beam. Results for plane wave incidence by a slit also come out of this solution. The remarkable simplicity and convenience of this method relative to alternative asymptotic procedures is discussed.