how to implement/overload binary operators for my class

Question

I have a problem. I create a program, which works on complex numbers, but I have a problem with overloading operators. My teacher said that I must create a lot of them, he said that I should check this link Why should I overload a C++ operator as a global function (STL does) and what are the caveats? 1) I must create 5 operators which are member function of class and which have one argument: +, −, !, ++, −−. Then

2) I must create 5 operators which are member function of class and which two arguments: =,+=, −=, *=, /=; Then

3) I must create 8 operators which are global friend function +, −, *, /, ==, !=, <<, >> and take two parameters.

My teacher said that I must change the declaration of these operators 2) and think about what they will do? Do you know how to change them?

    Comp operator=(const Comp x) = default;
    Comp operator-=(const Comp& x, int value)
    {
        x.real -= value;
        x.imag -= value;
        return x;
    } 
    Comp operator+=(const Comp& x, const Comp& y)
    {
        x.real += y.real;
        x.imag += y.imag;
        return x;
    }
    Comp operator*=(const Comp& x, const Comp& y)
    {
        x.real *= y.real;
        x.imag *= y.imag;
        return x;
    }
    Comp operator/=(const Comp& x, const Comp& y)
    {
        x.real /= y.real;
        x.imag /= y.imag;
        return x;
    } 

I get a lot of errors:

complex.cpp:74:45: error: ‘Comp Comp::operator-=(const Comp&, int)’ must take exactly one argument
     Comp operator-=(const Comp& x, int value)
                                             ^
complex.cpp:80:49: error: ‘Comp Comp::operator+=(const Comp&, const Comp&)’ must take exactly one argument
     Comp operator+=(const Comp& x, const Comp& y)
                                                 ^
complex.cpp:86:49: error: ‘Comp Comp::operator*=(const Comp&, const Comp&)’ must take exactly one argument
     Comp operator*=(const Comp& x, const Comp& y)
                                                 ^
complex.cpp:92:49: error: ‘Comp Comp::operator/=(const Comp&, const Comp&)’ must take exactly one argument
     Comp operator/=(const Comp& x, const Comp& y)
                                                 ^
complex.cpp:73:10: error: defaulted declaration ‘Comp Comp::operator=(Comp)’
     Comp operator=(const Comp x) = default;
          ^~~~~~~~
complex.cpp:73:10: error: does not match expected signature ‘constexpr Comp& Comp::operator=(Comp&)’

I also want to know is these operator are ok?

    Comp operator+(const Comp& x);
    Comp operator-(const Comp& x);
    bool operator!(void);
    const Comp& operator++()
    { 
        return *this;
    }
    const Comp operator++(int)
    { 
        Comp temp(*this); 
        operator++(); 
        return temp;  
    }
    const Comp& operator--()
    {
        return *this;
    }
    const Comp operator--(int)
    {
        Comp temp(*this); 
        operator--(); 
        return temp; 
    } 

This is my whole code

#include <fstream>
#include <cstdlib> 
#include <iostream>
#include <iomanip>
#include <cmath>
#ifndef M_PI
    #define M_PI 3.14159265358979323846
#endif
using namespace std;


class Comp {
    double real, imag;

public:
    Comp(){
    real=0;
    imag=0;
    }
    double re(void) const
    {
        return real;
    }
    double im(void) const
    {
        return imag;
    }
    double mod(void) const
    {
        return sqrt(re()*re() + im()*im());
    }
    double arg(void) const
    {
        double faza;
        if (im() >= 0)
            faza = acos(re()/mod());
        else
            faza = 2*M_PI - acos(re()/mod());

    return faza;
    }
    const Comp conj(void) const
    {
        Comp temp;
        temp.real = re();
        temp.imag = -im();
        return temp;
    }
    ~Comp(){}
    Comp operator+(const Comp& x);
    Comp operator-(const Comp& x);
    bool operator!(void);
    const Comp& operator++()
    { 
        return *this;
    }
    const Comp operator++(int)
    { 
        Comp temp(*this); 
        operator++(); 
        return temp;  
    }
    const Comp& operator--()
    {
        return *this;
    }
    const Comp operator--(int)
    {
        Comp temp(*this); 
        operator--(); 
        return temp; 
    } 
    Comp operator=(const Comp x) = default;
    Comp operator-=(const Comp& x, int value)
    {
        x.real -= value;
        x.imag -= value;
        return x;
    } 
    Comp operator+=(const Comp& x, const Comp& y)
    {
        x.real += y.real;
        x.imag += y.imag;
        return x;
    }
    Comp operator*=(const Comp& x, const Comp& y)
    {
        x.real *= y.real;
        x.imag *= y.imag;
        return x;
    }
    Comp operator/=(const Comp& x, const Comp& y)
    {
        x.real /= y.real;
        x.imag /= y.imag;
        return x;
    } 
    Comp operator=(const Comp x, const Comp y);
    Comp operator-=(const Comp& x, const Comp& y);
    Comp operator+=(const Comp& x, const Comp& y);
    Comp operator*=(const Comp& x, const Comp& y);
    Comp operator/=(const Comp& x, const Comp& y);

    friend const Comp operator+(const Comp& x, const Comp& y)
    {
        Comp temp;
        temp.real = x.real + y.real;
        temp.imag = x.imag + y.imag;
        return temp;
    }
    friend const Comp operator-(const Comp& x, const Comp& y)
    {
        Comp temp;
        temp.real = x.real - y.real;
        temp.imag = x.imag - y.imag;
        return temp;
    }
    friend const Comp operator*(const Comp& x, const Comp& y)
    {
        Comp temp;
        temp.real = x.real * y.real;
        temp.imag = x.imag * y.imag;
        return temp;
    }
    friend const Comp operator/(const Comp& x, const Comp& y)
    {
        Comp temp;
        temp.real = x.real / y.real;
        temp.imag = x.imag / y.imag;
        return temp;
    }
    friend bool operator==(const Comp& x, const Comp& y)
    {
        if (x.real == y.real && x.imag == y.imag)
            return 1;
        else
            return 0;
    }
    friend bool operator!=(const Comp& x, const Comp& y)
    {

        if (x.real != y.real || x.imag != y.imag)
            return 1;
        else
            return 0;
    }

    friend std::ostream& operator<<(std::ostream& wart1,  const Comp& a)
    {
        return wart1 <<fixed << setprecision(2) << '(' << a.re() << "," << a.im() << ')' << ' ' << endl;
    }
    friend std::istream& operator>>(std::istream& wart2, Comp& b){
        char c;
        return wart2>>c>>b.real>>c>>b.imag>>c; 
    }
};

int main(int argc, char* argv[])
{ 
    ifstream read(argv[1]);
    if (!read)
        { cerr << "Open error: " << argv[1] << endl; exit(1);}
    ofstream write(argv[2]);

    if(!write) { cerr << "Open error: " << argv[2] << endl; exit(2);} 
    read.clear();
    read.seekg(0);
    Comp x1;
    read >> x1;
    write << x1;
    cout << x1;
    Comp x2;
    read >> x2;
    write << x2;
    cout << x2;
    cout << x1.mod() << endl;
    cout << x2.mod() << endl;
    cout << x1.arg() << endl;
    cout << x2.arg() << endl;
    cout << x1.conj();
    cout << x2.conj();
    write << x2;
    write << x1.mod() << endl;
    write << x2.mod() << endl;
    write << x1.arg() << endl;
    write << x2.arg() << endl;
    write << x1.conj();
    write << x2.conj();
    Comp sum;
    sum = x1 + x2;
    cout << sum;
    write << sum;
    Comp sub;
    sub = x1 - x2;
    cout << sub;
    write << sub;
    Comp mult;
    mult = x1 * x2;
    cout << mult;
    write << mult;
    Comp div;
    div = x1 / x2;
    cout << div;
    write << div;

    return 0;
}  

Answer 1

You got the signature right for

Comp operator+(const Comp& x);
Comp operator-(const Comp& x);

but not for

Comp operator-=(const Comp& x, int value)

...and others.

When implemented as member functions, operators always operate on this. Ie your operator-= would be called as

Comp a,b;
a.operator-=(b,42);

but you want

a.operator-=(42);

Answer 2

Operator overloading is no different from other functions' overloading, so you must not change the function signature, but only its implementation. If that's a task for your university subject then go ahead and implement all the operators, otherwise you don't need to provide a custom version of all the operators for any class you build, but only when you really need them.