operator overloading and non-member functions c++

Question

I have written a class for complex numbers in which I have overloaded the operator + and everything works fine, however I need to implement this as a non-member function and I am not sure how, or why there is a benefit of doing so.

Here is my code .h:

class Complex
{
private:
    double a;
    double b;

public:
    Complex();
    Complex(double aGiven);
    Complex(double aGiven, double bGiven);

    double aGetValue();
    double bGetValue();    
    double operator[](bool getB);

    Complex add(Complex &secondRational);
    Complex operator+(Complex &secondRational);
}

.cpp:

Complex Complex::add(Complex &secondRational)
{
    double c = secondRational.aGetValue();
    double d = secondRational.bGetValue();
    double anew = a+c;
    double bnew = b+d;
    return Complex(anew,bnew);
}

Complex Complex::operator+(Complex &secondRational)
{
    return add(secondRational);
}

Any help on how to make these as non-member functions will be greatly appreciated!

Answer 1

Here is the addition operator outside of the class:

Complex operator+(const Complex& lhs, const Complex& rhs) {
  //implement the math to add the two
  return Complex(lhs.aGetValue() + rhs.aGetValue(),
                 lhs.bGetValue() + rhs.bGetValue());
}

Of course you will need to declare aGetValue() and bGetValue() as const:

double aGetValue() const {return a;}
double bGetValue() const {return b;}