c++设计复数类，实现复数的加减乘除

在 C++ 中，设计一个复数类（ComplexNumber），可以包括两个私有成员变量分别代表实部（real）和虚部（imaginary）。我们可以使用结构体或类来封装这两个属性，并提供公共的构造函数、赋值操作符以及加法、减法、乘法和除法等运算方法。下面是一个简单的例子：

#include <iostream>

// 定义复数类 ComplexNumber
class ComplexNumber {
private:
    double real;
    double imaginary;

public:
    // 构造函数
    ComplexNumber(double r = 0, double i = 0) : real(r), imaginary(i) {}

    // 赋值操作符
    ComplexNumber& operator=(const ComplexNumber& other) {
        if (this != &other) {
            real = other.real;
            imaginary = other.imaginary;
        }
        return *this;
    }

    // 友元函数实现复数加法
    friend ComplexNumber operator+(const ComplexNumber& a, const ComplexNumber& b) {
        double real_sum = a.real + b.real;
        double imag_sum = a.imaginary + b.imaginary;
        return ComplexNumber(real_sum, imag_sum);
    }

    // 友元函数实现复数减法
    friend ComplexNumber operator-(const ComplexNumber& a, const ComplexNumber& b) {
        double real_diff = a.real - b.real;
        double imag_diff = a.imaginary - b.imaginary;
        return ComplexNumber(real_diff, imag_diff);
    }

    // 友元函数实现复数乘法
    friend ComplexNumber operator*(const ComplexNumber& a, const ComplexNumber& b) {
        double real_prod = a.real * b.real - a.imaginary * b.imaginary;
        double imag_prod = a.real * b.imaginary + a.imaginary * b.real;
        return ComplexNumber(real_prod, imag_prod);
    }

    // 友元函数实现复数除法，需要处理分母为0的情况
    friend ComplexNumber operator/(const ComplexNumber& a, const ComplexNumber& b) {
        double denominator = b.real * b.real + b.imaginary * b.imaginary;
        if (denominator == 0) {
            throw std::runtime_error("Division by zero is not allowed.");
        }
        double real_quotient = (a.real * b.real + a.imaginary * b.imaginary) / denominator;
        double imag_quotient = (a.imaginary * b.real - a.real * b.imaginary) / denominator;
        return ComplexNumber(real_quotient, imag_quotient);
    }

    // 打印复数
    void print() const {
        std::cout << real << " + " << imaginary << "i" << std::endl;
    }
};

int main() {
    ComplexNumber c1(3, 4);
    ComplexNumber c2(1, 2);

    c1.print(); // 输出 3 + 4i
    c2.print(); // 输出 1 + 2i

    ComplexNumber sum = c1 + c2;
    ComplexNumber diff = c1 - c2;
    ComplexNumber prod = c1 * c2;
    ComplexNumber quot = c1 / c2; // 注意这里可能会抛出异常

    sum.print();
    diff.print();
    prod.print();

    try {
        quot.print();
    } catch (const std::exception& e) {
        std::cerr << "Caught exception: " << e.what() << std::endl;
    }

    return 0;
}

在这个例子中，`operator+`, `operator-`, `operator*`, 和 `operator/` 都是友元函数，它们允许我们像对待普通值一样对复数进行操作。注意，在除法运算中需要特别处理分母为零的情况。