Complex coordinate transformations are introduced for the analysis of time-harmonic electromagnetic wave propagation in perfectly matched double negative layers. The layer is perfectly matched to free space in the sense that any incident plane wave is transmitted through the free space-material interface without reflection, irrespective of the frequency and angle of incidence of the plane wave. The material constitutive parameters are obtained by mapping spatial coordinates into a manifold in complex space. The layer turns out to be anisotropic in general, and the special case where the medium is isotropic can be deduced from the coordinate transformations. The left-handedness, as well as the reversal in phase velocity appear naturally as a result of the mapping of the spatial coordinates into complex space. The consequences of this analysis are demonstrated by some examples.