用C++实现以下功能。14. 定义复数类COMPLEX，并用成员函数为复数类COMPLEX重载加、减及赋值运算符操作。 15. 写一个程序，定义一个抽象类Shape,由它派生3个类：Square(正方形)、Trapezoid（梯形）和Triangle三角形。用虚函数分别计算几种图形面积、并求它们的和。要求用基类指针数组，使它每一个元素指向一个派生类对象。

14. COMPLEX类定义如下：

class COMPLEX {
private:
    double real;
    double imag;
public:
    COMPLEX(double r = 0, double i = 0) : real(r), imag(i) {}
    COMPLEX operator+(const COMPLEX& c) const {
        return COMPLEX(real + c.real, imag + c.imag);
    }
    COMPLEX operator-(const COMPLEX& c) const {
        return COMPLEX(real - c.real, imag - c.imag);
    }
    COMPLEX& operator=(const COMPLEX& c) {
        if (this != &c) {
            real = c.real;
            imag = c.imag;
        }
        return *this;
    }
};

15. Shape类定义如下：

class Shape {
public:
    virtual double area() const = 0;
    virtual ~Shape() {}
};

class Square : public Shape {
private:
    double side;
public:
    Square(double s = 0) : side(s) {}
    double area() const {
        return side * side;
    }
};

class Trapezoid : public Shape {
private:
    double upper;
    double lower;
    double height;
public:
    Trapezoid(double u = 0, double l = 0, double h = 0) :
        upper(u), lower(l), height(h) {}
    double area() const {
        return (upper + lower) * height / 2;
    }
};

class Triangle : public Shape {
private:
    double base;
    double height;
public:
    Triangle(double b = 0, double h = 0) : base(b), height(h) {}
    double area() const {
        return base * height / 2;
    }
};

然后可以定义一个Shape类型的指针数组，每个元素指向一个派生类对象，计算它们的面积和，代码如下：

int main() {
    Shape* shapes[3];
    shapes[0] = new Square(5);
    shapes[1] = new Trapezoid(3, 5, 4);
    shapes[2] = new Triangle(4, 3);

    double sum = 0;
    for (int i = 0; i < 3; i++) {
        sum += shapes[i]->area();
    }

    std::cout << "The sum of areas is: " << sum << std::endl;

    for (int i = 0; i < 3; i++) {
        delete shapes[i];
    }

    return 0;
}