【项目-实现复数类中的运算符重载】 （1）请用类的成员函数，定义复数类重载运算符+、-、*、/，使之能用于复数的加减乘除

class Complex {public:    Complex(){real=0;imag=0;}    Complex(double r,double i){real=r; imag=i;}    Complex operator+(const Complex &c2);    Complex operator-(const Complex &c2);    Complex operator*(const Complex &c2);    Complex operator/(const Complex &c2);    void display();private:    double real;    double imag;};//下面定义成员函数//下面定义用于测试的main()函数int main(){    Complex c1(3,4),c2(5,-10),c3;    cout<<"c1=";    c1.display();    cout<<"c2=";    c2.display();    c3=c1+c2;    cout<<"c1+c2=";    c3.display();    c3=c1-c2;    cout<<"c1-c2=";    c3.display();    c3=c1*c2;    cout<<"c1*c2=";    c3.display();    c3=c1/c2;    cout<<"c1/c2=";    c3.display();    return 0;}

[参考解答]

#include 
      
       using namespace std;class Complex{public:    Complex(){real=0;imag=0;}    Complex(double r,double i){real=r; imag=i;}    Complex operator+(const Complex &c2);    Complex operator-(const Complex &c2);    Complex operator*(const Complex &c2);    Complex operator/(const Complex &c2);    void display();private:    double real;    double imag;};//下面定义成员函数//复数相加： (a+bi)+(c+di)=(a+c)+(b+d)i.Complex Complex::operator+(const Complex &c2){    Complex c;    c.real=real+c2.real;    c.imag=imag+c2.imag;    return c;}//复数相减：(a+bi)-(c+di)=(a-c)+(b-d)i.Complex Complex::operator-(const Complex &c2){    Complex c;    c.real=real-c2.real;    c.imag=imag-c2.imag;    return c;}//复数相乘：(a+bi)(c+di)=(ac－bd)+(bc+ad)i.Complex Complex::operator*(const Complex &c2){    Complex c;    c.real=real*c2.real-imag*c2.imag;    c.imag=imag*c2.real+real*c2.imag;    return c;}//复数相除：(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)iComplex Complex::operator/(const Complex &c2){    Complex c;    c.real=(real*c2.real+imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);    c.imag=(imag*c2.real-real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);    return c;}void Complex::display(){    cout<<"("<
       
        <<","<
        
         <<"i)"<
        
       
      

（2）请用类的友元函数，而不是成员函数，再次完成上面提及的运算符的重载；

[参考解答]

#include 
      
       using namespace std;class Complex{public:    Complex()    {        real=0;        imag=0;    }    Complex(double r,double i)    {        real=r;        imag=i;    }    friend Complex operator+(Complex &c1, Complex &c2);    friend Complex operator-(Complex &c1, Complex &c2);    friend Complex operator*(Complex &c1, Complex &c2);    friend Complex operator/(Complex &c1, Complex &c2);    void display();private:    double real;    double imag;};//复数相加：(a+bi)+(c+di)=(a+c)+(b+d)i.Complex operator+(Complex &c1, Complex &c2){    Complex c;    c.real=c1.real+c2.real;    c.imag=c1.imag+c2.imag;    return c;}//复数相减：(a+bi)-(c+di)=(a-c)+(b-d)i.Complex operator-(Complex &c1, Complex &c2){    Complex c;    c.real=c1.real-c2.real;    c.imag=c1.imag-c2.imag;    return c;}//复数相乘：(a+bi)(c+di)=(ac－bd)+(bc+ad)i.Complex operator*(Complex &c1, Complex &c2){    Complex c;    c.real=c1.real*c2.real-c1.imag*c2.imag;    c.imag=c1.imag*c2.real+c1.real*c2.imag;    return c;}//复数相除：(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)iComplex operator/(Complex &c1, Complex &c2){    Complex c;    c.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);    c.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);    return c;}void Complex::display(){    cout<<"("<
       
        <<","<
        
         <<"i)"<
        
       
      

　　事实上，运算符重载的函数还可以定义成一般函数，只不过这种做法并不好。下面给出使用一般函数完成运算符重载的程序。其中，加了序号的几处注释值得关注。

#include 
      
       using namespace std;class Complex{public:    Complex()    {        real=0;        imag=0;    }    Complex(double r,double i)    {        real=r;        imag=i;    }    double getReal() const    {        return real;   //(1)定义公用的数据接口，可以为const成员函数    }    double getImag() const    {        return imag;    }    void setReal(double r)    {        real=r;   //(1)定义公用的数据接口    }    void setImag(double i)    {        imag=i;    }    void display();private:    double real;    double imag;};//复数相加：(a+bi)+(c+di)=(a+c)+(b+d)i.Complex operator+(const Complex &c1, const Complex &c2) //(3)将参数处理为const更符合需求{    Complex c;    c.setReal(c1.getReal()+c2.getReal());   //(2)调用公用数据接口读取和修改私有数据成员    c.setImag(c1.getImag()+c2.getImag());    return c;}//复数相减：(a+bi)-(c+di)=(a-c)+(b-d)i.Complex operator-(const Complex &c1, const Complex &c2){    Complex c;    c.setReal(c1.getReal()-c2.getReal());    c.setImag(c1.getImag()-c2.getImag());    return c;}//复数相乘：(a+bi)(c+di)=(ac－bd)+(bc+ad)i.Complex operator*(const Complex &c1, const Complex &c2){    Complex c;    c.setReal(c1.getReal()*c2.getReal()-c1.getImag()*c2.getImag());    c.setImag(c1.getImag()*c2.getReal()+c1.getReal()*c2.getImag());    return c;}//复数相除：(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)iComplex operator/(const Complex &c1, const Complex &c2){    Complex c;    double d= (c2.getReal()*c2.getReal()+c2.getImag()*c2.getImag());    c.setReal((c1.getReal()*c2.getReal()+c1.getImag()*c2.getImag())/d);    c.setImag((c1.getImag()*c2.getReal()-c1.getReal()*c2.getImag())/d);    return c;}void Complex::display(){    cout<<"("<
       
        <<","<
        
         <<"i)"<
        
       
      

（3）定义一个定义完整的类（是可以当作独立的产品发布，成为众多项目中的“基础工程”）。这样的类在(2)的基础上，扩展+、-、*、/运算符的功能，使之能与double型数据进行运算。设Complex c; double d; c+d和d+c的结果为“将d视为实部为d的复数同c相加”，其他-、*、/运算符类似。 [参考解答]

#include 
     
      using namespace std;class Complex{public:    Complex()    {        real=0;        imag=0;    }    Complex(double r,double i)    {        real=r;        imag=i;    }    friend Complex operator+(Complex &c1, Complex &c2);    friend Complex operator+(double d1, Complex &c2);    friend Complex operator+(Complex &c1, double d2);    friend Complex operator-(Complex &c1, Complex &c2);    friend Complex operator-(double d1, Complex &c2);    friend Complex operator-(Complex &c1, double d2);    friend Complex operator*(Complex &c1, Complex &c2);    friend Complex operator*(double d1, Complex &c2);    friend Complex operator*(Complex &c1, double d2);    friend Complex operator/(Complex &c1, Complex &c2);    friend Complex operator/(double d1, Complex &c2);    friend Complex operator/(Complex &c1, double d2);    void display();private:    double real;    double imag;};//复数相加：(a+bi)+(c+di)=(a+c)+(b+d)i.Complex operator+(Complex &c1, Complex &c2){    Complex c;    c.real=c1.real+c2.real;    c.imag=c1.imag+c2.imag;    return c;}Complex operator+(double d1, Complex &c2){    Complex c(d1,0);    return c+c2; //按运算法则计算的确可以，但充分利用已经定义好的代码，既省人力，也避免引入新的错误，但可能机器的效率会不佳}Complex operator+(Complex &c1, double d2){    Complex c(d2,0);    return c1+c;}//复数相减：(a+bi)-(c+di)=(a-c)+(b-d)i.Complex operator-(Complex &c1, Complex &c2){    Complex c;    c.real=c1.real-c2.real;    c.imag=c1.imag-c2.imag;    return c;}Complex operator-(double d1, Complex &c2){    Complex c(d1,0);    return c-c2;}Complex operator-(Complex &c1, double d2){    Complex c(d2,0);    return c1-c;}//复数相乘：(a+bi)(c+di)=(ac－bd)+(bc+ad)i.Complex operator*(Complex &c1, Complex &c2){    Complex c;    c.real=c1.real*c2.real-c1.imag*c2.imag;    c.imag=c1.imag*c2.real+c1.real*c2.imag;    return c;}Complex operator*(double d1, Complex &c2){    Complex c(d1,0);    return c*c2;}Complex operator*(Complex &c1, double d2){    Complex c(d2,0);    return c1*c;}//复数相除：(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +(bc-ad)/(c^2+d^2)iComplex operator/(Complex &c1, Complex &c2){    Complex c;    c.real=(c1.real*c2.real+c1.imag*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);    c.imag=(c1.imag*c2.real-c1.real*c2.imag)/(c2.real*c2.real+c2.imag*c2.imag);    return c;}Complex operator/(double d1, Complex &c2){    Complex c(d1,0);    return c/c2;}Complex operator/(Complex &c1, double d2){    Complex c(d2,0);    return c1/c;}void Complex::display(){    cout<<"("<
      
       <<","<
       
        <<"i)"<