operator==

template<class T>
    bool operator==(const complex<T>& lhs, const complex<T>& rhs);
template<class T>
    bool operator==(const complex<T>& lhs, const T& rhs);
template<class T>
    bool operator==(const T& lhs, const complex<T>& rhs);

The operators each return true only if real(lhs) == real(rhs) && imag(lhs) == imag(rhs).