Scope problem in namespace and class, C++

Question

I tried to create a complex class in a C++ namespace per exercise, but when I try to define some methods of my class, the compiler returns error.

My code:

Complex. h:

#ifndef COMPLEX_N_H
#define COMPLEX_N_H
#include <iostream>
#include <math.h>

using namespace std;

namespace complex_number{
    class complex_N{
    public:
        virtual double real() const;
        virtual double imag() const;
        virtual double module() const;
        virtual double arg() const;
        virtual const complex_N operator +(const complex_N& z);
        virtual const complex_N operator -(const complex_N& z);
        virtual const complex_N operator *(const complex_N& z);
        virtual const complex_N operator /(const complex_N& z);
        virtual const bool operator ==(const complex_N& z);
        ostream& operator <<(ostream& outputStream);
    };
}


#endif // COMPLEX_H

complex_e. h:

#ifndef COMPLEX_E_H
#define COMPLEX_E_H
#include "complex.h"

namespace complex_number{
    class complex_e : public complex_N {
    public:
        complex_e();
        complex_e(double a);
        complex_e(double a, double b);
        double real() const;
        double imag() const;
        double module() const;
        double arg() const;
        complex_e conj() const;
        const complex_e operator +(const complex_e& z);
        const complex_e operator -(const complex_e& z);
        const complex_e operator *(const complex_e& z);
        const complex_e operator /(const complex_e& z);
        const bool operator ==(const complex_e& z);
    private:
        double re_;
        double im_;
    };
}

#endif

complex_e.cpp:

#include "complex_e.h"

complex_number::complex_e::complex_e():re_(0), im_(0){

}

complex_number::complex_e::complex_e(double a):re_(a), im_(0){

}

complex_number::complex_e::complex_e(double a, double b):re_(a), im_(b){

}

double complex_number::complex_e::real(){
    return re_;
}

double complex_number::complex_e::imag(){
    return im_;
}

double complex_number::complex_e::module(){
    return sqrt(re_*re_+im_*im_);
}

double complex_number::complex_e::arg(){
    return atan(im_/re_);
}

complex_number::complex_e complex_number::complex_e::conj(){
    return complex_number::complex_e(re_,-im_);
};

const complex_number::complex_e operator+(const complex_number::complex_e& z){
    return(complex_number::complex_e(z.re_+re_, z.im_+im_));
}

const complex_number::complex_e operator-(const complex_number::complex_e& z){
    return(complex_number::complex_e(re_-z.re_, im_-z.im_));
}

When I try to compile this code I get errors like:

Error 1: no declaration Matches 'double complex_number::complex_e:real()'

Error 2: no declaration Matches 'double complex_number::complex_e:imag()'

For all functions defined in complex_e.cpp, except constructors and operators.

Meanwhile, in the operators I set I get errors like:

error: 're_' was not declared in this Scope

error: 'im_' was not declared in this Scope

Whenre_ and im_ should be the private attributes of the object calling the constructors.