//  -----------------------------------------------------------------
//  -------             class Complex                ----------------
//  -------                                          ----------------
//  -------  2001 November 22     M.Vogel            ----------------
//  -----------------------------------------------------------------


class Complex {
	
	double a,b;
	public Complex() {  a=0 ;  b=0;  }
	public Complex(Complex c) { this.a=c.a ; this.b=c.b ; 	}
	public Complex(double x, double y) { this.a=x ; this.b=y ; }
	
	public double real(Complex x) {
		double z = x.a ;
		return(z);
	}
	
	public double imag(Complex x) {
		double z = x.b ;
		return(z);
	}
	
	public Complex conj(Complex x) {
		
		Complex z=new Complex();
		z.a= x.a ;
		z.b=-x.b ;
		return(z);
	}

	public Complex mult(Complex x, Complex y) {
		
		Complex z=new Complex();
		z.a=x.a*y.a-x.b*y.b;
		z.b=x.a*y.b+x.b*y.a;
		return(z);
	}

	public Complex mult(Complex x, double y) {
		
		Complex z=new Complex();
		z.a=x.a*y ;
		z.b=x.b*y ;
		
		return(z);
	}

	public Complex div(Complex x, Complex y) {
		
		Complex z=new Complex()       ;
		double b = y.betrag(y)        ;
		b = 1.0 / (b*b)               ;
		z = x.mult(x, y.conj(y))      ;
		z = z.mult(z, b )             ;
		
		return(z)                     ;
	}
	
	public Complex add(Complex x, Complex y) {
		
		Complex z=new Complex();
		z.a=x.a+y.a;
		z.b=x.b+y.b;
		
		return(z);		
	}

	public Complex add(Complex x, double y) {
		
		Complex z=new Complex();
		z.a=x.a+y ;
		z.b=x.b   ;
		
		return(z);		
	}
	
	public Complex sub(Complex x, Complex y) {
		
		Complex z=new Complex();
		z.a=x.a-y.a;
		z.b=x.b-y.b;
		
		return(z);		
	}

	public Complex sqrt(Complex x) {
		
		Complex z=new Complex()     ;
		double phi , r              ;
		r = x.betrag(x)             ;
		r = Math.sqrt(r)            ;
		phi = Math.atan2(x.b , x.a) ;
		phi = phi / 2.0             ;
		z.a = r * Math.cos(phi)     ;
		z.b = r * Math.sin(phi)     ;
		
		return(z);		
	}

	public double betrag(Complex x) {
	
		return(Math.sqrt(x.a*x.a+x.b*x.b));
		
	}
}