We extend the transformation-optics paradigm to a complex spatial coordinate domain, in order to deal with electromagnetic metamaterials characterized by balanced loss and gain, giving special emphasis to parity-time (PT) symmetric metamaterials. We apply this general theory to complex-source-point radiation and anisotropic transmission resonances, illustrating the capability and potentials of our approach in terms of systematic design, analytical modeling, and physical insights into complex-coordinate wave objects and resonant states.