Yes... but note that the final machine language code does use the processor opcodes that handle floats: MULSS, MOVSS

http://www.felixcloutier.com/x86/MULSS.html http://www.felixcloutier.com/x86/MOVSS.html

So the final float multiplication is done by the hardware. What the software does, is to (a) handle the complex number and convert it to floats, and probably (b) handle the double precision using single precision x86 opcodes.