An apparatus and method for multiplying packed real and imaginary components of complex numbers are described. A processor embodiment includes: a decoder to decode a first instruction to generate a decoded instruction; a first source register to store a first plurality of packed real and imaginary data elements; a second source register to store a second plurality of packed real and imaginary data elements; and execution circuitry to execute the decoded instruction. The execution circuitry includes: multiplier circuitry to select real and imaginary data elements in the first source register and second source, multiply each selected imaginary data element in the first source register with a selected real data element in the second source register, and multiply each selected real data element in the first source register with a selected imaginary data element in the second source register to generate a plurality of imaginary products; adder circuitry to add a first subset of the plurality of imaginary products and subtract a second subset of the plurality of imaginary products to generate a first temporary result, and to add a third subset of the plurality of imaginary products and subtract a fourth subset of the plurality of imaginary products to generate a second temporary result; and accumulation circuitry to combine the first temporary result with first data from a destination register to generate a first final result, combine the second temporary result with second data from the destination register to generate a second final result, and store the first final result and second final result back in the destination register.