An angle rotator uses a coarse stage rotation and a fine stage rotation to rotate an input complex signal in the complex plane according to an angle .theta.. The coarse stage rotation includes a memory device storing pre-computed cosine .theta..sub.M and sine .theta..sub.M values for fast retrieval, where .theta..sub.M is a radian angle that corresponds to a most significant word (MSW) of the input angle .theta.. The fine stage rotation uses one or more error values that compensate for approximations and quantization errors associated with the coarse stage rotation. The rotator consolidates operations into a small number of reduced-size multipliers, enabling efficient multiplier implementations such as Booth encoding, yielding a smaller and faster overall circuit.