import java.applet.Applet;
import java.awt.event.*;
import java.awt.*;

/**This class does the basic arithmetic of complex numbers */

public class Complex {
    double x,y;
    

    /**constructors **/

    public Complex() {
        this.x=0.0;
        this.y=0.0;
    } 

    public Complex(double x,double y) {
        this.x=x;
        this.y=y;
    }

    public Complex(Complex z) {
        this.x=z.x;
        this.y=z.y;
    }


    /**printout**/
     public void print() {
 	System.out.println("Complex: "+this.x+" "+this.y);
    } 



    /**basic arithmetic operations used in the proof **/

    public static Complex plus(Complex z1,Complex z2) {
        return new Complex(z1.x+z2.x, z1.y+z2.y);
    }

    public static Complex minus(Complex z1,Complex z2) {
        return new Complex(z1.x-z2.x, z1.y-z2.y);
    }

    public static double distMaxNorm(Complex a,Complex b) {
                  Complex z=minus(a,b);
	double t1=Math.abs(z.x);
	double t2=Math.abs(z.y);
	return(Math.max(t1,t2));
    }

    public static Complex average(Complex z1,Complex z2) {
        return new Complex(.5*z1.x+.5*z2.x, .5*z1.y+.5*z2.y);
    }



    /**these are not used in the proof**/

    public static Complex times(Complex z1,Complex z2) {
        return new Complex(z1.x*z2.x-z1.y*z2.y,
        z1.x*z2.y+z1.y*z2.x);
    }

      public static Complex inverse(Complex z) {
         double d=z.x*z.x+z.y*z.y;
         return new Complex(z.x/d,-z.y/d);
     }

     public static Complex divide(Complex z1,Complex z2) {
         return times(z1,inverse(z2));
     }
    


}