The invention concerns a complex number multiplier receiving the binary number A, B, C and D complimentarily coded in pairs so as to perform the complex multiplication (A+jB)*(C+jD). A first processing stage enables to perform the operations A-B, C-D, and A+B whereof the results are binary numbers in base two with a redundant binary format, and a borrow-save coding for subtractions and carry-save coding for addition. A second processing stage converts said results into coded binary numbers in base four. A third processing stage enables to perform multiplication (A-B)C, (C-D)B and (A+B)D with a redundant binary format and a borrow-save coding. A last stage comprises two adders for working out the real part (A-B)C+(C-D)B and the imaginary part (A+B)D+(C-D)B in a redundant binary format and a borrow-save coding.