I'm not entirely satisfied that the way it is calculated by C++11/C99 is correct. (Although I can see the appeal of the C version.) Mathematically, complex multiplication (a+bj)*x should be identical to (a+bj)*(x+0j), but obviously in the presence of NANs that is no longer the case. So it isn't clear to me that Python is wrong to allow NANs to "infect" the real part after multiplication.

Before changing the behaviour, I'd like to hear from someone who might be able to comment on what the IEEE-754 standard may have to say about this.