复数：是指能写成如下形式的数a+bi,这里a和b是实数，i是虚数单位， i*i = -1

在复数 a+bi 中 a为复式的实部 ， b为复数的虚部

复数的四则运算:

（a+bi）+ （c+di）= （a+c）+ （b+d）i； 

（a+bi）- （c+di） = （a-c） + （b-d）i；

（a+bi）* （c+di） = （ac-bd）+ （ad+bc）i；

（a+bi）/ （c+di）= (（ac+bd）+（bc-ad）i） / （c*c+d*d）；

程序代码:

#include <iostream>

using namespace std;

template<class T>//类声明前加模板的声明

class Complex   
{
public:
      Complex( )
      {
          real=0;
          imag=0;
      }      
     
      Complex(T r,T i)
      {
          real=r;
          imag=i;
      }
     
      Complex complex_add(Complex &c2);//复数的加法
      Complex complex_minus(Complex &c2);//复数的减法
      Complex complex_multiply(Complex &c2);//复数的乘法
      Complex complex_divide(Complex &c2);//复数的除法
      void display( );//显示复数

private:
      T real;//复数的实部
      T imag;//复数的虚部
};

template<class T>
Complex<T> Complex<T>::complex_add(Complex &c2)//复数的加法
{
    Complex c3;

    c3.real  = real + c2.real;
    c3.imag  = imag + c2.imag;

    return c3;
}

template<class T>
Complex<T> Complex<T>::complex_minus(Complex &c2)//复数的减法
{
    Complex c3;

    c3.real  = real - c2.real;
    c3.imag  = imag - c2.imag;

    return c3;
}

template<class T>
Complex<T> Complex<T>::complex_multiply(Complex &c2)//复数的乘法
{
    Complex c3;

    c3.real = real*c2.real - imag * c2.imag;
    c3.imag = real*c2.imag + imag * c2.real;

    return c3;
}

template<class T>
Complex<T> Complex<T>::complex_divide(Complex &c2)//复数的除法
{  
    Complex c3;

    c3.real = (real * c2.real + imag * c2.imag) / (c2.real*c2.real + c2.imag * c2.imag);

    c3.imag = (imag * c2.real - real * c2.imag) / (c2.real*c2.real + c2.imag * c2.imag);

    return c3;
}

template<class T>
void Complex<T>::display( )//显示复数
{
   
    if(imag > 0)//当虚部大于0时
    {
        cout<<real<<'+'<<imag<<'i';
    }
    else if(0 == imag)//当虚部等于0时
    {
        cout<<real;
    }
    else//当虚部小于0时
    {
        cout<<real<<imag<<'i';
    }
}

int main( )
{
    Complex<double> Cmp1(8,-2), Cmp2(7,10), Cmp3;
   
    //两个复数相加
    Cmp1.display();
    cout<<" + ";
    Cmp2.display();
    cout<<" = ";
    Cmp3 = Cmp1.complex_add(Cmp2);
    Cmp3.display();
    cout<<endl;

    //两个复数相减
    Cmp1.display();
    cout<<" - ";
    Cmp2.display();
    cout<<" = ";
    Cmp3 = Cmp1.complex_minus(Cmp2);
    Cmp3.display();
    cout<<endl;

    //两个复数相乘
    Cmp1.display();
    cout<<" * ";
    Cmp2.display();
    cout<<" = ";
    Cmp3 = Cmp1.complex_multiply(Cmp2);
    Cmp3.display();
    cout<<endl;

    //两个复数相除
    Cmp1.display();
    cout<<" / ";
    Cmp2.display();
    cout<<" = ";
    Cmp3 = Cmp1.complex_divide(Cmp2);
    Cmp3.display();
    cout<<endl;

    system("pause");
}

执行结果: