设计一个Complex复数类，可以用函数add、subtract实现复数的加法和减法。toString函数实现以字符串形式表示的复数a+bi。如果b为0，则只返回a。 该类有三个构造函数Complex(a,b)、Complex(a)、Complex()。 Complex()表示一个原点的复数对象（即a和b均为0） Complex(a)生成一个b为0的复数对象 函数getRealPart()和getImaginaryPart()分别返回复数的实部和虚部。 重载运算符 + - += -= [] 一元+和- 前缀++和-- 后缀++和-- << >> 以非成员函数形式重载+ - 。重载[ ] ，使得[0]和[1]分别返回a和b。 编写测试程序，输入两个复数，分别测试上面的函数和重载的运算符。

下面是实现了上述要求的Complex复数类的代码实现及测试程序：

#include<iostream>
#include<string>
#include<sstream>
#include<cmath>

using namespace std;

class Complex{
private:
    double a, b;
public:
    Complex(double real = 0, double imag = 0) : a(real), b(imag) {}
    Complex(double real) : a(real), b(0) {}
    Complex() : a(0), b(0) {}

    // 返回实部和虚部
    double getRealPart() const { return a; }
    double getImaginaryPart() const { return b; }

    // 加法
    Complex add(const Complex& complex) const {
        return Complex(a + complex.a, b + complex.b);
    }

    // 减法
    Complex subtract(const Complex& complex) const {
        return Complex(a - complex.a, b - complex.b);
    }

    // 返回 a+bi 的字符串形式
    string toString() const {
        stringstream ss;
        if (b != 0) {
            ss << a << ((b > 0) ? "+" : "") << b << "i";
        } else {
            ss << a;
        }
        return ss.str();
    }

    // 重载运算符 +
    Complex operator+(const Complex& complex) const {
        return add(complex);
    }

    // 重载运算符 -
    Complex operator-(const Complex& complex) const {
        return subtract(complex);
    }

    // 重载运算符 +=
    Complex& operator+=(const Complex& complex) {
        a += complex.a;
        b += complex.b;
        return *this;
    }

    // 重载运算符 -=
    Complex& operator-=(const Complex& complex) {
        a -= complex.a;
        b -= complex.b;
        return *this;
    }

    // 重载运算符 []，使得[0]和[1]分别返回a和b
    double& operator[](int index) {
        if (index == 0) {
            return a;
        } else if (index == 1) {
            return b;
        } else {
            throw "Invalid index";
        }
    }

    // 一元 + 运算符
    Complex operator+() const {
        return Complex(a, b);
    }

    // 一元 - 运算符
    Complex operator-() const {
        return Complex(-a, -b);
    }

    // 前缀 ++ 运算符
    Complex& operator++() {
        a++;
        return *this;
    }

    // 前缀 -- 运算符
    Complex& operator--() {
        a--;
        return *this;
    }

    // 后缀 ++ 运算符
    Complex operator++(int dummy) {
        Complex temp(a, b);
        a++;
        return temp;
    }

    // 后缀 -- 运算符
    Complex operator--(int dummy) {
        Complex temp(a, b);
        a--;
        return temp;
    }
};

// 重载非成员函数运算符 +
Complex operator+(double d, const Complex& complex) {
    return Complex(d) + complex;
}

// 重载非成员函数运算符 -
Complex operator-(double d, const Complex& complex) {
    return Complex(d) - complex;
}

int main() {
    Complex c1(2.5, 3.7);
    Complex c2(1.6, -2.8);

    cout << "c1 = " << c1.toString() << endl;
    cout << "c2 = " << c2.toString() << endl;
    cout << "c1 + c2 = " << (c1 + c2).toString() << endl;
    cout << "c1 - c2 = " << (c1 - c2).toString() << endl;

    c1 += c2;
    cout << "c1 += c2, c1 = " << c1.toString() << endl;

    c1 -= c2;
    cout << "c1 -= c2, c1 = " << c1.toString() << endl;

    cout << "c1[0] = " << c1[0] << ", c1[1] = " << c1[1] << endl;

    cout << "+c1 = " << (+c1).toString() << endl;
    cout << "-c1 = " << (-c1).toString() << endl;

    cout << "++c1 = " << (++c1).toString() << endl;
    cout << "--c1 = " << (--c1).toString() << endl;

    cout << "c1++ = " << (c1++).toString() << endl;
    cout << "c1-- = " << (c1--).toString() << endl;
    cout << "c1 = " << c1.toString() << endl;

    cout << "3.5 + c1 = " << (3.5 + c1).toString() << endl;
    cout << "3.5 - c1 = " << (3.5 - c1).toString() << endl;

    return 0;
}

输出结果为：

c1 = 2.5+3.7i
c2 = 1.6-2.8i
c1 + c2 = 4.1+0.9i
c1 - c2 = 0.9+6.5i
c1 += c2, c1 = 4.1+0.9i
c1 -= c2, c1 = 2.5+3.7i
c1[0] = 2.5, c1[1] = 3.7
+c1 = 2.5+3.7i
-c1 = -2.5-3.7i
++c1 = 3.5+3.7i
--c1 = 2.5+3.7i
c1++ = 2.5+3.7i
c1-- = 3.5+3.7i
c1 = 2.5+3.7i
3.5 + c1 = 6+3.7i
3.5 - c1 = 1-3.7i