> There aren't to my knowledge any CPUs with special instructions for complex numbers
There are lots of processors out there besides CPUs. You could even design a new processor or program an FPGA to do complex math. Fast Fourier transforms deal with imaginary math, for example. You can do those in a number of ways, including on a CPU or GPU, but it's not unheard of for companies to use either custom hardware or programmable hardware to meet performance needs.
There are lots of processors out there besides CPUs. You could even design a new processor or program an FPGA to do complex math. Fast Fourier transforms deal with imaginary math, for example. You can do those in a number of ways, including on a CPU or GPU, but it's not unheard of for companies to use either custom hardware or programmable hardware to meet performance needs.