#ifndef INCLUDE_Quaternion
#define INCLUDE_Quaternion
#include <complex>
#include <vector>
#include <iostream>
using namespace std;
typedef std::complex<double> Complex;

class Quaternion{
private:
	Complex alpha,beta;
public:
	Quaternion( double r , double i1 = 0 , double i2 = 0 , double i3 = 0 ) 
		: alpha( r , i1 ) , beta( i2 , i3 ) {}
	Quaternion( Complex c1 , Complex c2 = 0 ) : alpha( c1 ) , beta( c2 ) {}
	Quaternion(  ) : alpha( 0 , 0 ) , beta( 0 , 0 ) {}
	bool operator==( const Quaternion & c ) const ;
	bool operator!=( const Quaternion & c ) const ;
	Quaternion & operator=( const Quaternion & c ) ;
	Quaternion & operator+=( const Quaternion & c ) ;
	Quaternion & operator-=( const Quaternion & c ) ;
	Quaternion & operator*=( const Quaternion & c ) ;
	Quaternion & operator/=( const Quaternion & c ) ;
	double real( ) const { return alpha.real() ; } 
	double imag( int i ) const ;

	Quaternion operator + ( ) const { return *this ; } 
	Quaternion operator + ( Quaternion c ) const ;
	Quaternion operator - ( ) const ;
	Quaternion operator - ( Quaternion c ) const ;
	Quaternion operator * ( Quaternion c ) const ;
	Quaternion operator / ( Quaternion c ) const ;
	Quaternion conj( ) const ;
	double abs() const ;
	double norm() const ;
};

std::ostream &operator<<(std::ostream & , const Quaternion & );

#endif