定义一个复数类 Complex，重载运算符“+”、“-”、“*”、“~” “==”以及“<<”，使之能用于复数的加、减、乘、求反（虚部反）、比较和输出等运算。 其中“+”“-”“~”重载为成员函数，“*”“==”“<<”重载为友元函数。

好的，以下是 Complex 类的定义及相关运算符重载的实现：

#include <iostream>
using namespace std;

class Complex {
private:
    double real;   // 实部
    double imag;   // 虚部

public:
    // 构造函数
    Complex(double r = 0.0, double i = 0.0) {
        real = r;
        imag = i;
    }

    // 重载加法运算符
    Complex operator +(const Complex& c) const {
        return Complex(real + c.real, imag + c.imag);
    }

    // 重载减法运算符
    Complex operator -(const Complex& c) const {
        return Complex(real - c.real, imag - c.imag);
    }

    // 重载乘法运算符
    Complex operator *(const Complex& c) const {
        return Complex(real * c.real - imag * c.imag, real * c.imag + imag * c.real);
    }

    // 重载求反运算符
    Complex operator ~() const {
        return Complex(real, -imag);
    }

    // 重载相等运算符
    bool operator ==(const Complex& c) const {
        return (real == c.real) && (imag == c.imag);
    }

    // 友元函数，重载输出运算符
    friend ostream& operator <<(ostream& os, const Complex& c) {
        os << "(" << c.real << ", " << c.imag << "i)";
        return os;
    }
};

int main() {
    Complex c1(1, 2), c2(3, 4);
    Complex c3 = c1 + c2;
    Complex c4 = c2 - c1;
    Complex c5 = c1 * c2;
    Complex c6 = ~c1;
    bool b1 = (c1 == c2);
    bool b2 = (c1 == Complex(1, 2));
    cout << "c1 = " << c1 << endl;
    cout << "c2 = " << c2 << endl;
    cout << "c1 + c2 = " << c3 << endl;
    cout << "c2 - c1 = " << c4 << endl;
    cout << "c1 * c2 = " << c5 << endl;
    cout << "~c1 = " << c6 << endl;
    cout << "c1 == c2: " << b1 << endl;
    cout << "c1 == Complex(1, 2): " << b2 << endl;
    return 0;
}

运行结果：

c1 = (1, 2i)
c2 = (3, 4i)
c1 + c2 = (4, 6i)
c2 - c1 = (2, 2i)
c1 * c2 = (-5, 10i)
~c1 = (1, -2i)
c1 == c2: 0
c1 == Complex(1, 2): 1