import java.io.*;

// class complex
//   complex number abstraction
//
class complex {
    // constructors
public complex()
{
nreal=0;
nimag=0;
}
    
public complex(double nre,double nim)
{
nreal=nre;
nimag=nim;
}
    
public complex(double numer)
{
nreal=numer;
nimag=0;
}

public complex(complex value )
{
nreal=value.real();
nimag=value.imaginary();
}
    // accessor functions

public double real() 
{
return nreal;
}

public double imaginary() 
{
return nimag;
}

public double R() 
{
return Math.sqrt(nreal*nreal+nimag*nimag);
}

public double theta()
{
return Math.atan2(nimag,nreal);
}

public double dtheta()
{
return Math.atan2(nimag,nreal)*45.0/Math.atan(1.0);
}
    
    // assignments
public void assign(complex right)
{
nreal=right.real();
nimag=right.imaginary();
}

public void add(complex  right)
{
nimag = nimag + right.imaginary();
nreal = nreal + right.real();
}

public void substract(complex right)
{
nimag = nimag - right.imaginary();
nreal = nreal - right.real();
}

public void multiply(complex right )
{
nreal = nreal*right.real() - nimag*right.imaginary();
nimag = nreal*right.imaginary() +  nimag*right.real();
}

public void divide(complex right )
{
double a=nreal*nreal+nimag*nimag;
nreal = ( nreal*right.real() +  nimag*right.imaginary())/a;
nimag = (-nreal*right.imaginary() +  nimag*right.real())/a;
}

public static complex add(complex left, complex right)
{ // return sum of two complex numbers
 double r1=(left.real() + right.real());
 double i1=(left.imaginary() + right.imaginary());
 complex result;
 result=new complex(r1,i1);
 return result;
}

public static complex substract(complex left, complex right)
{ // return substraction of two complex numbers
 complex result;
 result=new complex((left.real() - right.real()),
                (left.imaginary() - right.imaginary()));
 return result;
}

public static complex multiply(complex left, complex right)
{ // return multiplication of two complex numbers
 complex result;
 result=new complex
 ((left.real()*right.real() - left.imaginary()*right.imaginary()),
  (left.real()*right.imaginary() + left.imaginary()*right.real()));
return result;
}


public static complex divide(complex left, complex  right)
{ // return division of two complex numbers
 double a=right.real()*right.real()+right.imaginary()*right.imaginary();
 complex result;
 result=new complex
 ((left.real()*right.real()  + left.imaginary()*right.imaginary())/a,
  (-left.real()*right.imaginary() + left.imaginary()*right.real())/a);
 return result;
}

public static complex pow(complex left, double right)
{ // return sum of two complex numbers
 double Rad,th;
 Rad=Math.pow(left.R(),right);
 th=right*left.theta();
 complex result;
 result =new complex((Rad*Math.cos(th) ),
                (Rad*Math.sin(th) )  );
 return result;
}

public boolean smaller(complex left,complex right)
{
// less then comparison of two complex numbers
return (left.R() < right.R());
}

public boolean smaller_equal(complex left,complex right)
{
// less then and equal comparison of two complex numbers
return (left.R() <= right.R());
}

public boolean greater(complex left,complex right)
{
// greater then comparison of two complex numbers
return left.R() > right.R();
}

public boolean greater_equal(complex left,complex  right)
{
// greater then and equal comparison of two complex numbers
return left.R() >= right.R();
}


public boolean equal(complex left,complex right)
{
// equal comparison of two complex numbers
return left.R() == right.R();
}

public boolean not_equal(complex left,complex  right)
{
// not equal comparison of two complex numbers
return left.R() != right.R();
}

public static String toString(complex  value)
{
String b="";
if(Math.abs(value.imaginary())!=1)
  {
  if(value.imaginary() >= 0)
    b=b+"("+value.real()+" + "+value.imaginary()+"i )";
  else
    b=b+"("+value.real()+" - "+(-value.imaginary())+"i )"; 
  }
else
  {
  if(value.imaginary() >= 0)
    b=b+"("+value.real()+" + i )";
  else
    b=b+"("+value.real()+" - i )";
}
return b;
}

public String toString()
{
String b="";
if(Math.abs(imaginary())!=1)
  {
  if(imaginary() >= 0)
    b=b+"("+real()+" + "+imaginary()+"i )";
  else
    b=b+"("+real()+" - "+(-imaginary())+"i )"; 
  }
else
  {
  if(imaginary() >= 0)
    b=b+"("+real()+" + i )";
  else
    b=b+"("+real()+" - i )";
}
return b;
}


    // data areas
    public double   nreal;
    public double   nimag;

                };