The important thing is that the C++ class overloads operators and mathematical functions, and the C class doesn't.
Example: http://coliru.stacked-crooked.com/view?id=0d295064bd367eca
Source: http://en.cppreference.com/w/c/numeric/complex
Have you tried that? Of course Microsoft refuses to implement C99, so you could only try it on non-Microsoft C implementations.
The important thing is that the C++ class overloads operators and mathematical functions, and the C class doesn't.