【C++】数据结构：抽象定义复数，并实现复数的加、减、乘、除四则运算,用complex写

在C++中，可以使用内置的`<complex>`库来方便地处理复数。这个库提供了一个名为`complex`的数据类型，用于表示复数。下面是如何使用`complex`定义一个复数并实现基本算术操作的一个简单示例：

#include <iostream>
#include <complex>

// 定义复数类
class ComplexNumber {
public:
    // 构造函数
    std::complex<double> c; // 使用complex双精度类型存储实部和虚部

    // 构造复数
    ComplexNumber(double real = 0, double imag = 0) : c(real, imag) {}

    // 加法
    ComplexNumber operator+(const ComplexNumber& other) const {
        return ComplexNumber(c.real() + other.c.real(), c.imag() + other.c.imag());
    }

    // 减法
    ComplexNumber operator-(const ComplexNumber& other) const {
        return ComplexNumber(c.real() - other.c.real(), c.imag() - other.c.imag());
    }

    // 乘法
    ComplexNumber operator*(const ComplexNumber& other) const {
        double real = c.real() * other.c.real() - c.imag() * other.c.imag();
        double imag = c.real() * other.c.imag() + c.imag() * other.c.real();
        return ComplexNumber(real, imag);
    }

    // 除法，这里假设除数不为零
    ComplexNumber operator/(const ComplexNumber& other) const {
        double denominator = other.c.real() * other.c.real() + other.c.imag() * other.c.imag();
        return ComplexNumber((c.real() * other.c.real() + c.imag() * other.c.imag()) / denominator,
                            (c.imag() * other.c.real() - c.real() * other.c.imag()) / denominator);
    }

    // 输出复数
    void print() const {
        std::cout << "Complex Number (" << c.real() << ", " << c.imag() << "i)" << std::endl;
    }
};

int main() {
    ComplexNumber a(2, 3);
    ComplexNumber b(4, -1);

    ComplexNumber sum = a + b;
    ComplexNumber diff = a - b;
    ComplexNumber prod = a * b;
    ComplexNumber quot = a / b;

    std::cout << "Sum: ";
    a.print();
    b.print();
    sum.print();

    std::cout << "\nDifference: ";
    a.print();
    b.print();
    diff.print();

    std::cout << "\nProduct: ";
    a.print();
    b.print();
    prod.print();

    std::cout << "\nQuotient (assuming non-zero denominator): ";
    a.print();
    b.print();
    quot.print();

    return 0;
}

在这个例子中，我们首先定义了一个`ComplexNumber`类，它包含一个`std::complex<double>`类型的成员变量`c`。然后实现了加、减、乘、除四种运算符重载，以及一个打印复数的方法。在`main()`函数里，创建了两个复数对象并进行了相应的计算。