【C++】实现复数类的重载

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复数类的功能及要求

复数对于从小学习数学的我们并不陌生，其操作性相对比较简单。复数类主要考察的是我们对运算符重载的熟练程度，主要有四则运算的+、-、×、/，以及+=、-=、>、<、==、!=前置++，后置++的运算符重载。复数类共有两个参数，实部(_real)与虚部(_imag)，因此需要定义两个成员变量，具体的实现思路如下。

复数类的设计思路

设计思路主要针对复数的四则运算展开：即+、-、×、/。复数的加法+、减法-遵守的规则为实部-实部，虚部-虚部，乘法的运算规则为(a+bi)(c+di)=(ac-bd)+(bc+ad)i ,除法较为复杂，运算规则为：(a+bi)/(c+di)，化简为：(a+bi)(c-di)/(c+di)(c-di) = ((ac+bd)+(bc-ad)i)/(c^2+d2)。除此之外的运算符重载比较简单，具体实现过程如下。

参考代码

complex.h

#include <iostream>
#include <Windows.h>
using namespace std;
class Complex
{
public:
	Complex(double real,double imag)
		:_real(real)
		,_imag(imag)
	{}
	Complex(const Complex& t)
	{
		_real = t._real;
		_imag = t._imag;
	}
	~Complex()
	{}
	//运算符的重载
	Complex& operator=(const Complex& t);
	bool operator==(const Complex& t);
	bool operator>(const Complex& t);
	bool operator<(const Complex& t);
	bool operator!=(const Complex& t);
	bool operator>=(const Complex& t);
	bool operator<=(const Complex& t);
	Complex operator++();
	Complex operator++(int);
	Complex& operator+=(const Complex& t);
	Complex& operator-=(const Complex& t);
	Complex operator+(const Complex& t);
	Complex operator-(const Complex& t);
	Complex operator*(const Complex& t);
	Complex operator/(const Complex& t);
	friend ostream& operator<<(ostream& _cout,const Complex& c);
private:
	double _real;
	double _imag;
};

main.cpp

#include "complex.h"
void FunTest()
{
	Complex c1(1,2);
	Complex c2(3,4);
	Complex c3 = c1*c2;
	Complex c4 = ++c1;
	Complex c5 = c2++;
	Complex c6 = c2/c1;
	cout<<c3<<endl;
	cout<<c4<<endl;
	cout<<c5<<endl;
	cout<<c6<<endl;
}
int main()
{
	FunTest();
	system("pause");
	return 0;
}

complex.cpp

#include "complex.h"
//=
Complex& Complex::operator=(const Complex& t)
{
	if(this != &t)
	{
		_real = t._real;
		_imag = t._imag;
	}
	return *this;
}
bool Complex::operator==(const Complex& t)
{
	if(_imag != 0 || t._imag != 0)
	{
		cout<<"虚部不为0，无法比较!"<<endl;
		return false;
	}
	return (_real == t._real)&&(_imag == t._imag);
}
bool Complex::operator!=(const Complex& t)
{
	return !(*this == t);
}
bool Complex::operator>(const Complex& t)
{
	if(_imag != 0 || t._imag != 0)
	{
		cout<<"虚部不为0，无法比较大小！"<<endl;
		return false;
	}
	else
	{
		if(_real > t._real)
			return true;
		return false;
	}
}
bool Complex::operator<(const Complex& t)
{
	if(_imag != 0 || t._imag != 0)
	{
		cout<<"虚部不为0，无法比较大小！"<<endl;
		return false;
	}
	return !(*this >= t);
}
bool Complex::operator>=(const Complex& t)
{
	if(_imag != 0 || t._imag != 0)
	{
		cout<<"虚部不为0，无法比较大小！"<<endl;
		return false;
	}
	return (*this == t)||(*this > t);
}
bool Complex::operator<=(const Complex& t)
{
	if(_imag != 0 || t._imag != 0)
	{
		cout<<"虚部不为0，无法比较大小!"<<endl;
		return false;
	}
	return (*this == t)||(*this < t);
}
Complex& Complex::operator+=(const Complex& t)
{
	_real += t._real;
	_imag += t._imag;
	return *this;
}
Complex& Complex::operator-=(const Complex& t)
{
	_real -= t._real;
	_imag -= t._imag;
	return *this;
}
Complex Complex::operator+(const Complex& t)
{
	Complex temp(*this);
	temp._real += t._real;
	temp._imag += t._imag;
	return temp;
}
Complex Complex::operator-(const Complex& t)
{
	Complex temp(*this);
	temp._real -= t._real;
	temp._imag -= t._imag;
	return temp;
}
Complex Complex::operator*(const Complex& t)//(a+bi)(c+di)=(ac-bd)+(bc+ad)i
{
	Complex temp(*this);
	temp._real = this->_real*t._real - this->_imag*t._imag;
	temp._imag = this->_imag*t._real + this->_real*t._imag;
	return temp;
}
Complex Complex::operator/(const Complex& t)//(a+bi)(c-di)/(c+di)(c-di)
{
	Complex temp(*this);
	temp._real = (this->_real*t._real+this->_imag*t._imag)/(t._real*t._real+t._imag*t._imag)\
		+(this->_imag*t._real - this->_real*t._imag)/((t._real*t._real+t._imag*t._imag));
	return temp;
}
Complex Complex::operator++()
{
	++_real;
	++_imag;
	return *this;
}
Complex Complex::operator++(int)
{
	Complex temp(*this);
	_real++;
	_imag++;
	return temp;
}
ostream& operator<<(ostream& _cout,const Complex& t)
{
	_cout<<t._real<<"+"<<t._imag<<"i"<<endl;
	return _cout;
}