定义一个复数类Complex，复数的实部Real与虚部Image定义为私有数据成员。

Question

定义一个复数类Complex，复数的实部Real与虚部Image定义为私有数据成员。用复数类定义复数对象c1、c2、c3。友元函数add,sub,mul,div分别用于复数的加、减、乘、除法运算，用公有成员函数Dispaly()显示复数运算结果。在主函数中，实例化两个复数，并输入一个运算符，按照运算符选择相应的友远函数进行复数运算，然后输出结果。

Answer 1

这个问题唯一的难题就是运算法则

1. 加法：(a + bi) + (c + di) = (a + c) + (b + d)i
2. 减法：(a + bi) - (c + di) = (a - c) + (b- d)i
3. 乘法：(a + bi) * (c + di) = (a*c - b*d) + (b*c + a*d)i
4. 除法：(a + bi) / (c + di) = ((a*c + b*d) / (c*c + d*d)) + ((b*c - a*d) / (c*c + d*d))i

#include <iostream>

using namespace std;

class Complex
{
    public:
        Complex(){Real = 0.0; Image = 0.0;}                                   // 默认构造函数
        Complex(double x, double y) : Real(x), Image(y) {}    // 拷贝构造函数 
        ~Complex(){}
        friend Complex Add(const Complex& c1, const Complex& c2);
        friend Complex Sub(const Complex& c1, const Complex& c2);
        friend Complex Mul(const Complex& c1, const Complex& c2);
        friend Complex Div(const Complex& c1, const Complex& c2);
        void display();
    private:
        double Real;
        double Image;
};

Complex Add(const Complex& c1, const Complex& c2)
{
    Complex m;
    m.Real = c1.Real + c2.Real;
    m.Image = c1.Image + c2.Image;
    return m;
}

Complex Sub(const Complex& c1, const Complex& c2)
{
    Complex m;
    m.Real = c1.Real - c2.Real;
    m.Image = c1.Image - c2.Image;
    return m;
}

Complex Mul(const Complex& c1, const Complex& c2)
{ 
    Complex m;
    m.Real = c1.Real * c2.Real - c1.Image * c2.Image;
    m.Image = c1.Real * c2.Image + c1.Image * c2.Real;
    return m;
}

Complex Div(const Complex& c1, const Complex& c2)
{
    Complex m;
    m.Real = (c1.Real * c2.Real + c1.Image * c2.Image) / (c2.Real * c2.Real + c2.Image * c2.Image);
    m.Image = (c1.Image * c2.Real - c1.Real * c2.Image) / (c2.Real * c2.Real + c2.Image * c2.Image);
    return m;
}

void    Complex::display()
{
    cout << Real << " + " << Image << "i" << endl;
}

int main()
{
    Complex c1(6, 8);
    Complex c2(2, 4);
    Complex c3;
    char c = 'a';
    
    while (c != 'c')
    {
        cout << "Please input [+ - * /]: ";
        cin >> c;
        if (c == '+')
        {
            c3 = Add(c1, c2);
            c3.display();
        }
        else if (c == '-')
        {
            c3 = Sub(c1, c2);
            c3.display();
        }
        else if (c == '*')
        {
            c3 = Mul(c1, c2);
            c3.display();
        }
        else if (c == '/')
        {
            c3 = Div(c1, c2);
            c3.display();
        }
        else
        {
            cout << "Error character, pleae input again." << endl;
        }
    } 

    return 0;
}