C++中的复数类是一种用于表示和操作复数的自定义数据类型。复数由实部和虚部组成，可以表示为a + bi的形式，其中a是实部，b是虚部，i是虚数单位。

下面是一个简单的复数类的实现示例：

#include <iostream>

class Complex {
private:
    double real; // 实部
    double imaginary; // 虚部

public:
    // 默认构造函数
    Complex() {
        real = 0.0;
        imaginary = 0.0;
    }

    // 带参构造函数
    Complex(double r, double i) {
        real = r;
        imaginary = i;
    }

    // 获取实部
    double getReal() const {
        return real;
    }

    // 获取虚部
    double getImaginary() const {
        return imaginary;
    }

    // 重载加法运算符
    Complex operator+(const Complex& other) const {
        Complex result;
        result.real = real + other.real;
        result.imaginary = imaginary + other.imaginary;
        return result;
    }

    // 重载减法运算符
    Complex operator-(const Complex& other) const {
        Complex result;
        result.real = real - other.real;
        result.imaginary = imaginary - other.imaginary;
        return result;
    }

    // 重载乘法运算符
    Complex operator*(const Complex& other) const {
        Complex result;
        result.real = real * other.real - imaginary * other.imaginary;
        result.imaginary = real * other.imaginary + imaginary * other.real;
        return result;
    }

    // 重载输出运算符
    friend std::ostream& operator<<(std::ostream& os, const Complex& c) {
        os << c.real << " + " << c.imaginary << "i";
        return os;
    }
};

int main() {
    Complex c1(2.0, 3.0);
    Complex c2(1.0, 2.0);

    Complex sum = c1 + c2;
    Complex difference = c1 - c2;
    Complex product = c1 * c2;

    std::cout << "c1: " << c1 << std::endl;
    std::cout << "c2: " << c2 << std::endl;
    std::cout << "Sum: " << sum << std::endl;
    std::cout << "Difference: " << difference << std::endl;
    std::cout << "Product: " << product << std::endl;

    return 0;
}

在上面的示例中，Complex类封装了两个私有成员变量real和imaginary，分别表示复数的实部和虚部。它提供了默认构造函数和带参构造函数来初始化复数对象。

Complex类还重载了加法运算符、减法运算符和乘法运算符，使得可以方便地进行复数的加减乘操作。此外，还重载了输出运算符<<，以便能够直接输出复数对象的内容。

在main函数中，我们创建了两个Complex对象c1和c2，并使用重载的加法运算符、减法运算符和乘法运算符进行复数的加减乘操作。最后，我们输出了这些操作的结果。

需要注意的是，这只是一个简单的复数类的实现示例，实际的复数类可以根据需求进行扩展和优化

实例——complex的实现

#include <iostream>
using namespace std;
class complex{
public:
    complex(double real = 0.0, double imag = 0.0): m_real(real), m_imag(imag){ };
public:
    friend complex operator+(const complex & A, const complex & B);
    friend complex operator-(const complex & A, const complex & B);
    friend complex operator*(const complex & A, const complex & B);
    friend complex operator/(const complex & A, const complex & B);
    friend istream & operator>>(istream & in, complex & A);
    friend ostream & operator<<(ostream & out, complex & A);
private:
    double m_real;  //实部
    double m_imag;  //虚部
};
//重载加法运算符
complex operator+(const complex & A, const complex &B){
    complex C;
    C.m_real = A.m_real + B.m_real;
    C.m_imag = A.m_imag + B.m_imag;
    return C;
}
//重载减法运算符
complex operator-(const complex & A, const complex &B){
    complex C;
    C.m_real = A.m_real - B.m_real;
    C.m_imag = A.m_imag - B.m_imag;
    return C;
}
//重载乘法运算符
complex operator*(const complex & A, const complex &B){
    complex C;
    C.m_real = A.m_real * B.m_real - A.m_imag * B.m_imag;
    C.m_imag = A.m_imag * B.m_real + A.m_real * B.m_imag;
    return C;
}
//重载除法运算符
complex operator/(const complex & A, const complex & B){
    complex C;
    double square = A.m_real * A.m_real + A.m_imag * A.m_imag;
    C.m_real = (A.m_real * B.m_real + A.m_imag * B.m_imag)/square;
    C.m_imag = (A.m_imag * B.m_real - A.m_real * B.m_imag)/square;
    return C;
}
//重载输入运算符
istream & operator>>(istream & in, complex & A){
    in >> A.m_real >> A.m_imag;
    return in;
}
//重载输出运算符
ostream & operator<<(ostream & out, complex & A){
    out << A.m_real <<" + "<< A.m_imag <<" i ";;
    return out;
}
int main(){
    complex c1, c2, c3;
    cin>>c1>>c2;
    c3 = c1 + c2;
    cout<<"c1 + c2 = "<<c3<<endl;
    c3 = c1 - c2;
    cout<<"c1 - c2 = "<<c3<<endl;
    c3 = c1 * c2;
    cout<<"c1 * c2 = "<<c3<<endl;
    c3 = c1 / c2;
    cout<<"c1 / c2 = "<<c3<<endl;
    return 0;
}