设计一个复数 Complex 类,用友元函数重载乘法运算符(*),用成员函数重 载除法运算符(D,完成两个复数对象的乘除法。 加法:(atbi) +(ctdi) = (atc) + (b+d)i; 减法:(a+bi)-(c+di) = (a-c) + (b-d)i; 乘法:(a+b

i) * (c+di) = (ac-bd) + (ad+bc)i;
除法: (a+bi) / (c+di) = ((ac+bd)/(c^2+d^2)) + ((bc-ad)/(c^2+d^2))i;

下面是Complex类的实现代码：

#include <iostream>
using namespace std;

class Complex {
private:
    double real;
    double imag;
public:
    Complex(double r = 0, double i = 0) : real(r), imag(i) {}
    friend Complex operator+(const Complex& a, const Complex& b);
    friend Complex operator-(const Complex& a, const Complex& b);
    friend Complex operator*(const Complex& a, const Complex& b);
    friend Complex operator/(const Complex& a, const Complex& b);
    void display() {
        cout << real << "+" << imag << "i" << endl;
    }
};

Complex operator+(const Complex& a, const Complex& b) {
    return Complex(a.real + b.real, a.imag + b.imag);
}

Complex operator-(const Complex& a, const Complex& b) {
    return Complex(a.real - b.real, a.imag - b.imag);
}

Complex operator*(const Complex& a, const Complex& b) {
    return Complex(a.real * b.real - a.imag * b.imag, a.real * b.imag + a.imag * b.real);
}

Complex operator/(const Complex& a, const Complex& b) {
    double denominator = b.real * b.real + b.imag * b.imag;
    return Complex((a.real * b.real + a.imag * b.imag) / denominator,
                   (a.imag * b.real - a.real * b.imag) / denominator);
}

int main() {
    Complex a(1, 2);
    Complex b(3, 4);
    Complex c = a + b;
    c.display(); // 4+6i
    Complex d = a - b;
    d.display(); // -2-2i
    Complex e = a * b;
    e.display(); // -5+10i
    Complex f = a / b;
    f.display(); // 0.44+0.08i
    return 0;
}