复数类（Class Complex）c++的简单实现

本文主要根据候捷《面向对象高级开发》课程实现的一个复数类。
所涉及的功能有 加减乘（除法我高中没学过）、以及对应的+=、-=、*=。还有取模、取反、求共轭复数、判断是否相同、输出等。
代码将分模块的进行讲述，不想看可以直接滑到文末。文末会给出完整代码。

首先，实现的是类的初始化及对其数据成员的访问。
由于访问数据成员并不会修改其相应的值，可以设置为常函数。

class Complex {
public:
    Complex(double x, double y) : re(x), im(y){}
    Complex() : re(0), im(0){}
    double real() const { return re; }
    double imag() const { return im; }

private:
    double re, im;
};

取模，即输出 r e 2 + i m 2 sqrt {re^2 +im^2} re2+im2 ​

class Complex {
public:
    double length() {
        return pow(this->re * this->re + this->im * this->im, 0.5);
    }
private:
    double re, im;
};

共轭复数，即实部相同，虚部互为相反数。
求共轭复数，并不会改变原复数。故不返回引用类型。

class Complex {
public:
    Complex conj() {
        return Complex(this->re, -this->im);
    }
private:
    double re, im;
};

先实现的是在原对象基础上修改的操作，+=，-=，*=。在原对象的基础上与另一个对象进行运算。
根据相关的运算性质，有着如下的代码。

class Complex {
public:
    Complex &operator+=(const Complex &c);
    Complex &operator-=(const Complex &c);
    Complex &operator*=(const Complex &c);

private:
    double re, im;
    friend Complex &_plus(Complex *, const Complex &);
    friend Complex &_minus(Complex *, const Complex &);
    friend Complex &_times(Complex *, const Complex &);
};
//  + 
inline Complex &_plus(Complex *ths, const Complex &c) {
    ths->re += c.re;
    ths->im += c.im;
    return *ths;
}
// += Complex
inline Complex & Complex::operator += (const Complex & c) {
    return _plus(this, c);
}
//  - 
inline Complex &_minus (Complex *ths, const Complex &c) {
    ths->re -= c.re;
    ths->im -= c.im;
    return *ths;
}
// -= Complex
inline Complex & Complex::operator -= (const Complex & c) {
    return _minus(this, c);
}
//  * 
inline Complex &_times(Complex *ths, const Complex &c) {
    ths->re = ths->re * c.re - ths->im * c.im;
    ths->im = ths->re * c.im + ths->im * c.re;
    return *ths;
}
// *= Complex
inline Complex & Complex::operator*=(const Complex & c) {
    return _times(this, c);
}

此外，还写出了相应的与纯实数进行运算。（纯实数可以是一个int、double等基本数据类型，而纯虚数是实部为0的对象，故不重复实现）

class Complex {
public:
    template 
    Complex &operator+=(const T num);
    template 
    Complex &operator-=(const T num);
    template 
    Complex &operator*=(const T num);

private:
    double re, im;
};
// += number
template 
inline Complex & Complex::operator += (const T num) {
    this->re += num;
    return *this;
}
// -= number
template 
inline Complex & Complex::operator -= (const T num) {
    this->re -= num;
    return *this;
}
// *=number
template 
inline Complex & Complex::operator *= (const T num) {
    this->re *= num;
    this->im *= num;
    return *this;
}

重载完带=的运算符后，开始重载基本的运算符，定义了三个基本操作 +-*分别实现两个复数间的+-*
由于在类内部尝试重载时，发生相应的错误（参数个数过多），于是在类的外部定义了相应的功能函数。
在该部分，考虑到运算符左右的参数类型的问题，同样进行了重载。

//Complex + Complex
inline Complex  operator+ (const Complex & x,const Complex & y) {
    return Complex(x.real() + y.real(), x.imag() + y.imag());
}
// Complex + number
template 
inline Complex operator+(const Complex &c, T num) {
    return Complex(c.real() + num, c.imag());
}
// number + Complex
template 
inline Complex operator+(T num, const Complex &c) {
    return Complex(c.real() + num, c.imag());
}
//Complex - Complex
inline Complex operator-(const Complex &x, const Complex &y) {
    return Complex(x.real() - y.real(), x.imag() - y.imag());
}
// Complex - number
template 
inline Complex operator-(const Complex &c, T num) {
    return Complex(c.real() - num, c.imag());
}
// number - Complex
template 
inline Complex operator-(T num, const Complex &c) {
    return Complex(num - c.real(), -c.imag());
}
// Complex * Complex
inline Complex operator*(const Complex &x, const Complex &y) {
    return Complex(x.real() * y.real() - x.imag() * y.imag(), x.real() * y.imag() + x.imag() * y.real());

}
// Complex * number
template 
inline Complex operator*(const Complex &c, T num) {
    return Complex(c.real() * num, c.imag() * num);
}
// number * Complex
template 
inline Complex operator*(T num, const Complex &c) {
    return Complex(c.real() * num, c.imag() * num);
}

私以为取反是用来赋值，故并未修改原对象的成员变量。

// -Complex
inline Complex operator-(const Complex &c) {
    return Complex(-c.real(), -c.imag());
}

实部虚部完全相同为相等，任一个不同则为不同。

// ==
inline bool operator==(const Complex &x, const Complex &y) {
    return (x.real() == y.real()) && (x.imag() == y.imag());
}
// !=
inline bool operator!=(const Complex &x, const Complex &y) {
    // return !(x == y);   //不是相同则为不同
    return (x.real() != y.real()) || (x.imag() != y.imag());
}

输出的格式为a+b i，考虑到美观性，额外的判断了下a==0 b==0 b < 0的情况。即，0+3i、1+0i、1+（-3）i类型特殊化处理。

inline ostream& operator <<(ostream& os,const Complex & c) {
    if (c.real() && c.imag()) {
        if (c.imag() >0) {
            return os << c.real() << "+" << c.imag() << "i";
        } else {
            return os << c.real() << c.imag() << "i";
        }
    } else if (c.real()) {
        return os << c.real();
    } else {
        return os << c.imag() << "i";
    }
}

#include
using namespace std;
class Complex {
public:
    Complex(double x, double y) : re(x), im(y){}
    Complex() : re(0), im(0){}
    double real() const { return re; }
    double imag() const { return im; }
    Complex &operator+=(const Complex &c);
    template 
    Complex &operator+=(const T num);

    Complex &operator-=(const Complex &c);
    template 
    Complex &operator-=(const T num);

    Complex &operator*=(const Complex &c);
    template 
    Complex &operator*=(const T num);

    Complex conj() {
        return Complex(this->re, -this->im);
    }

    double length() {
        return pow(this->re * this->re + this->im * this->im, 0.5);
    }

private:
    double re, im;
    friend Complex &_plus(Complex *, const Complex &);
    friend Complex &_minus(Complex *, const Complex &);
    friend Complex &_times(Complex *, const Complex &);
};
//  + 
inline Complex &_plus(Complex *ths, const Complex &c) {
    ths->re += c.re;
    ths->im += c.im;
    return *ths;
}
//  - 
inline Complex &_minus (Complex *ths, const Complex &c) {
    ths->re -= c.re;
    ths->im -= c.im;
    return *ths;
}
//  * 
inline Complex &_times(Complex *ths, const Complex &c) {
    ths->re = ths->re * c.re - ths->im * c.im;
    ths->im = ths->re * c.im + ths->im * c.re;
    return *ths;
}
// += Complex
inline Complex & Complex::operator += (const Complex & c) {
    return _plus(this, c);
}
// += number
template 
inline Complex & Complex::operator += (const T num) {
    this->re += num;
    return *this;
}

// -= Complex
inline Complex & Complex::operator -= (const Complex & c) {
    return _minus(this, c);
}
// -= number
template 
inline Complex & Complex::operator -= (const T num) {
    this->re -= num;
    return *this;
}
// *= Complex
inline Complex & Complex::operator*=(const Complex & c) {
    return _times(this, c);
}
// *=number
template 
inline Complex & Complex::operator *= (const T num) {
    this->re *= num;
    this->im *= num;
    return *this;
}
//Complex + Complex
inline Complex  operator+ (const Complex & x,const Complex & y) {
    return Complex(x.real() + y.real(), x.imag() + y.imag());
}
// Complex + number
template 
inline Complex operator+(const Complex &c, T num) {
    return Complex(c.real() + num, c.imag());
}
// number + Complex
template 
inline Complex operator+(T num, const Complex &c) {
    return Complex(c.real() + num, c.imag());
}
//Complex - Complex
inline Complex operator-(const Complex &x, const Complex &y) {
    return Complex(x.real() - y.real(), x.imag() - y.imag());
}
// Complex - number
template 
inline Complex operator-(const Complex &c, T num) {
    return Complex(c.real() - num, c.imag());
}
// number - Complex
template 
inline Complex operator-(T num, const Complex &c) {
    return Complex(num - c.real(), -c.imag());
}
// -Complex
inline Complex operator-(const Complex &c) {
    return Complex(-c.real(), -c.imag());
}
// Complex * Complex
inline Complex operator*(const Complex &x, const Complex &y) {
    return Complex(x.real() * y.real() - x.imag() * y.imag(), x.real() * y.imag() + x.imag() * y.real());

}
// Complex * number
template 
inline Complex operator*(const Complex &c, T num) {
    return Complex(c.real() * num, c.imag() * num);
}
// number * Complex
template 
inline Complex operator*(T num, const Complex &c) {
    return Complex(c.real() * num, c.imag() * num);
}
inline ostream& operator <<(ostream& os,const Complex & c) {
    if (c.real() && c.imag()) {
        if (c.imag() >0) {
            return os << c.real() << "+" << c.imag() << "i";
        } else {
            return os << c.real() << c.imag() << "i";
        }
    } else if (c.real()) {
        return os << c.real();
    } else {
        return os << c.imag() << "i";
    }
}
// ==
inline bool operator==(const Complex &x, const Complex &y) {
    return (x.real() == y.real()) && (x.imag() == y.imag());
}
// !=
inline bool operator!=(const Complex &x, const Complex &y) {
    // return !(x == y);   //不是相同则为不同
    return (x.real() != y.real()) || (x.imag() != y.imag());
}

int main() {
    Complex x(3,4);
    Complex y(3, -4);
    cout << x.length() << endl;
    cout << x * y << endl;
    x += 2;
    cout << x << endl;
    cout << -x << endl;
    cout << (x == y.conj())<