Interesting. I went to WolframAlpha, and entered "(6+4i)mod(3+5i)" and was given the answer "-2+2i." Assuming what you said to be true, I don't know how that answer was generated, but it is more like what I am looking for than 0 for any complex number.

To explain why I ask this, I am writing a calculator. It uses postfix notation, and operates on arbitrary precision complex numbers. One of the operations that is defined is modulus, and I would like it to work for all inputs, rather than just all real inputs. Since WolframAlpha does not tell me how it arrived at it's result, I can only hope that someone here can.