An apparatus and method for multiplying packed real and imaginary components of complex numbers. A method comprises: multiplying selected imaginary and real data elements in a first and second source registers to generate a plurality of imaginary products; adding a first subset of the plurality of imaginary products to generate a first temporary result and adding a second subset of the plurality of imaginary products to generate a second temporary result; negating the first temporary result to generate a third temporary result and the second temporary result to generate a fourth temporary result; accumulating the third temporary result with first data to generate a first final result and accumulating the fourth temporary result with second data to generate a second final result; and storing the first final result and second final.