定义复数类的乘法与除法

Question

定义复数类的乘法与除法，使之能执行下列运算：

(正文打不出来，只好用图片代替)

Answer 1

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为了实现一个复数类并支持乘法和除法操作，你需要创建一个新的C++类，包含复数的实部和虚部，并提供必要的成员函数来执行所需的运算。下面是一个详细的步骤，包括类定义、构造函数、赋值运算符重载、乘法运算符重载、除法运算符重载以及主程序示例。

首先，创建一个名为Complex的头文件（Complex.h）：

#ifndef COMPLEX_H
#define COMPLEX_H

class Complex {
public:
    // 构造函数
    Complex(double real = 0.0, double imaginary = 0.0);

    // 赋值运算符重载
    Complex& operator=(const Complex& other);

    // 加法运算符重载（这里只展示，实际项目中需要实现）
    Complex operator+(const Complex& other) const;

    // 减法运算符重载（这里只展示，实际项目中需要实现）
    Complex operator-(const Complex& other) const;

    // 乘法运算符重载
    Complex operator*(const Complex& other) const;
    Complex operator*(double scalar) const;
    friend Complex operator*(double scalar, const Complex& complex);

    // 除法运算符重载
    Complex operator/(const Complex& other) const;
    Complex operator/(double scalar) const;
    friend Complex operator/(double scalar, const Complex& complex);

    // 获取复数的实部和虚部
    double getReal() const { return real; }
    double getImaginary() const { return imaginary; }

private:
    double real;
    double imaginary;
};

#endif // COMPLEX_H

接下来，实现这个类的成员函数（Complex.cpp）：

#include "Complex.h"

// 构造函数
Complex::Complex(double real, double imaginary)
    : real(real), imaginary(imaginary) {}

// 赋值运算符重载
Complex& Complex::operator=(const Complex& other) {
    if (this != &other) {
        real = other.real;
        imaginary = other.imaginary;
    }
    return *this;
}

// 乘法运算符重载
Complex Complex::operator*(const Complex& other) const {
    double newReal = real * other.real - imaginary * other.imaginary;
    double newImaginary = real * other.imaginary + imaginary * other.real;
    return Complex(newReal, newImaginary);
}

Complex Complex::operator*(double scalar) const {
    return Complex(real * scalar, imaginary * scalar);
}

Complex operator*(double scalar, const Complex& complex) {
    return complex * scalar;
}

// 除法运算符重载
Complex Complex::operator/(const Complex& other) const {
    double denominator = other.real * other.real + other.imaginary * other.imaginary;
    double newReal = (real * other.real + imaginary * other.imaginary) / denominator;
    double newImaginary = (imaginary * other.real - real * other.imaginary) / denominator;
    return Complex(newReal, newImaginary);
}

Complex Complex::operator/(double scalar) const {
    return Complex(real / scalar, imaginary / scalar);
}

Complex operator/(double scalar, const Complex& complex) {
    return Complex(scalar) / complex;
}

最后，在主程序中测试这些操作（main.cpp）：

#include <iostream>
#include "Complex.h"

int main() {
    Complex a(2.0, 5.0), b(7.0, 8.0), c(0.0, 0.0);

    // 测试乘法
    c = a * b;
    std::cout << "a * b: (" << c.getReal() << ", " << c.getImaginary() << ")\n";

    // 测试与标量相乘
    c = a * 2.0;
    std::cout << "a * 2.0: (" << c.getReal() << ", " << c.getImaginary() << ")\n";
    
    c = 2.0 * a;
    std::cout << "2.0 * a: (" << c.getReal() << ", " << c.getImaginary() << ")\n";

    // 测试除法
    c = a / b;
    std::cout << "a / b: (" << c.getReal() << ", " << c.getImaginary() << ")\n";

    c = a / 2.0;
    std::cout << "a / 2.0: (" << c.getReal() << ", " << c.getImaginary() << ")\n";

    c = 2.0 / a;
    std::cout << "2.0 / a: (" << c.getReal() << ", " << c.getImaginary() << ")\n";

    return 0;
}

将这三个文件（Complex.h, Complex.cpp, main.cpp）放在同一个目录下，然后编译并运行main.cpp，你会得到乘法和除法的结果。注意，这里没有处理除以零的情况，这在实际应用中需要特别关注。