The design of slot arrays requiring nonuniform phase distributions, such as those having shaped beam radiation patterns, are facilitated by the development of slots having independent amplitude and phase control. A "complex" slot (which is inclined and displaced) on the broad wall of a rectangular waveguide makes it possible to control the coupling characteristics over a range in phase from zero to2piand over a range in magnitude from zero to unity. The "voltage" across the slot as a function of its orientation is found and is related to the coupling parameters used in common array design. An experimental procedure for independently verifying the amplitude and phase characteristics is described. A typical complex slot array design is made and radiation patterns are included demonstrating the accuracy and usefulness of the design procedure.