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The direct digital multiplication of complex numbers is examined. The proposed technique bypasses the classical method based on the identity (A+Bj)(C+Dj)=AC-BD+(AD+BC)j. The complex multiplication is considered as one operation and is examined in the bit-level. Various multipliers, such as the parallel or serial-parallel types and the realisation through microprogramming on an arithmetic unit, are presented, all of which are based on the above technique.