Are you sure it compiles? I noticed that my statement was inaccurate since std::complex is not a container, but still, references are not copyable (though what they refer to may be copyable). So, what happens if you try to assign a std::complex<double&> to another std::complex<double&>? It would mean that you have to assign the references themselves so they refer to a different object, and as pointed out this is illegal.
It does compile however, but I've not tried to use it. What would the problem be? It seems like most of the natural complex op.s would work.