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#include "iostream"
#include "math.h"
using namespace std;
 
class Complex 
{
   double re, im; 
   
 
   
   Complex() {};
   
   Complex (double r) 
   {
      re = r; 
      im = 0;
   }
   
   Complex (double r, double i) 
   {
      re = r; 
      im = i;
   } 
   
   Complex (Complex &c)
   {
      re = c.re; 
      im = c.im;
   }
   
   ~Complex() {}
   
   double abs() 
   {
      return sqrt(re * re - im * im);
   }     
 
   Complex & operator = (Complex &c)
   {
      re = c.re;
      im = c.im;
 
      return (*this);
   }
 
   Complex Complex::operator + (Complex &c)
   {
      Complex temp;
 
      temp.re = re + c.re;
      temp.im = im + c.re;
 
      return temp;
   }
 
   Complex Complex::operator - (Complex &c)
   {
      Complex temp;
 
      temp.re = re - c.re;
      temp.im = im - c.re;
    
      return temp;
   }
 
   Complex Complex::operator * (Complex &c) 
   {
      Complex temp;
 
      temp.re = re*c.re;
      temp.im = re*c.im;
 
      return temp;
   }
 
   Complex Complex::operator / (Complex &c) 
   {
      Complex temp;
 
      double r = c.re * c.re + c.im * c.im;
      temp.re = (re * c.re + im * c.im) / r;
      temp.re = (im * c.re - re * c.im) / r;
 
      return temp;
   }   
 
   friend ostream &operator<<(ostream &, Complex &);
   friend istream &operator>>(istream &, Complex &); 
 
};
 
ostream &operator<<(ostream &out, Complex &c)
{
   out << "(" << c.re << ") + I (" << c.im << "\n";
   
   return out;
}
 
istream &operator>>(istream &in, Complex &c)
{
   in >> c.re >> c.im;
   
   return in;
}
 
 
class ComplexExt
{
public:
friend ComplexExt operator + (Complex &a1, Complex &b1);
friend ComplexExt operator - (Complex &a1, Complex &b1);
friend ComplexExt operator * (Complex &a1, Complex &b1);
friend ComplexExt operator / (Complex &a1, Complex &b1);
friend ComplexExt operator & (Complex &a1, Complex &b1);
friend ComplexExt operator &&(Complex &a1,Complex &b1);
friend ComplexExt operator == (Complex &a1,Complex &b1);
void ShowComplex();
public:
ComplexExt (void);
ComplexExt (double a1, double b1);
~ ComplexExt (void);
int n;
public:
double re;
double im;
};
ComplexExt:: ComplexExt (void)
{
}
ComplexExt:: ComplexExt (double a, double b)
{
re=a;
im=b;
}
ComplexExt::~ ComplexExt (void)
{
}
ComplexExt operator + (ComplexExt &a, ComplexExt &b){
double re = a.re + b.re;
double im = a.im + b.im;
cout << "Summa arif.forma: " << re << " + " << im << "i" << endl;
double f1=sqrt(re*re+im*im);
double f2=re/f1;
double f3=im/f1;
cout << "Trigonom summa" << endl;
cout << f1 << "(cos(" << f2 << ") + isin(" << f3 << "))" << endl;
ComplexExt t(re,im);
return t;
}
ComplexExt operator - (ComplexExt &a, ComplexExt &b){
 
double re = a.re - b.re;
double im = a.im - b.im;
cout << "Raznost': " << re << " + " << im << "i" << endl;
double f1=sqrt(re*re+im*im);
double f2=re/f1;
double f3=im/f1;
cout << "Trigonom raznost'" << endl;
cout << f1 << "(cos(" << f2 << ") + isin(" << f3 << "))" << endl;
ComplexExt t(re,im);
return t;
}
ComplexExt operator * (ComplexExt &a, ComplexExt &b){
double re = a.re*b.re - a.im*b.im;
double im = a.im*b.re+a.re*b.im;
cout << "Proizvedenie: " << re << " + " << im << "i" << endl;
double f1=sqrt(re*re+im*im);
double f2=re/f1;
double f3=im/f1;
cout << "Trigonom proiz." << endl;
cout << f1 << "(cos(" << f2 << ") + isin(" << f3 << "))" << endl;
ComplexExt t(re,im);
return t;
}
ComplexExt operator / (ComplexExt &a, ComplexExt &b){
if(b.re*b.re+b.im*b.im==0)
{
cout <<"Delenie na 0";
}
else{
double re=(a.re*b.re+a.im+b.im)/(b.re*b.re+b.im*b.im);
double im=(a.im*b.re-a.re*b.im)/(b.re*b.re+b.im*b.im);
cout << "Chasnoe: " << re << " + " << im << "i" << endl;
double f1=sqrt(re*re+im*im);
double f2=re/f1;
double f3=im/f1;
cout << "Trigonom chastnoe" << endl;
cout << f1 << "(cos(" << f2 << ") + isin(" << f3 << "))" << endl;
ComplexExt t(re, im);
return t;
}
}
ComplexExt operator &( ComplexExt &a, ComplexExt &b){
int n;
cout << "Vvedite chislo stepeni:" << endl;
cin >> n;
double r=sqrt(a.re*a.re+a.im*a.im);
double rn=pow(2,r);
double f2=n*a.re/rn;
double f3=n*a.im/rn;
cout << "Trigonom form vozvedenie v stepen' a:" << endl;
cout << rn << "(cos(" << f2 << ") + isin(" << f3 << "))" << endl;
ComplexExt t(n,rn);
return t;
}
ComplexExt operator &&( ComplexExt &a, ComplexExt &b){
int m;
int k;
cout << "Vvedite chislo ctepeni korny:" << endl;
cin >> m;
cout << "Vvedite nomer korny:" << endl;
cin >> k;
double r=sqrt(a.re*a.re+a.im*a.im);
 
double rn=pow(2,r);
double f1=(m*a.re/rn+2*3,14*k)/m;
double f2=(m*a.im/rn+2*3.14*k)/m;
cout << "Trigonom form vyshislenie korny a:" << endl;
cout << rn << "(cos(" << f1 << ") + isin(" << f2 << "))" << endl;
ComplexExt t(m,k);
return t;
}
ComplexExt operator == (ComplexExt &a, ComplexExt &b){
double r=sqrt(a.re*a.re+a.im*a.im);
double f2=a.re/r;
cout << "Eksponenta a:" << endl;
cout << r << "e^(i*" << f2 << ")" << endl;
ComplexExt t(r,f2);
return t;
}
void ComplexExt::ShowComplex(){
cout << "Vvedite chislo" <<endl;
cin >> re;
cin >> im;
cout << "Arif. forma: " << re << " + " << im << "i" << endl;
double z=sqrt(re*re+im*im);
cout << "Modul' shisla:" << z << endl;
cout << "Trigonom form" << endl;
double f=re/z;
double f1=im/z;
cout << z << "(cos(" << f << ") + isin(" << f1 << "))" << endl;
}