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

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

public class XtraComplex {
    double x,y;

    public static double norm(Complex z) {
        return Math.sqrt(z.x*z.x+z.y*z.y);
    }

    public static Complex unit(Complex z) {
        double d=norm(z);
        return new Complex(z.x/d,z.y/d);
    }

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

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

    public static double dist(Complex a,Complex b) {
        Complex z=minus(a,b);
        return(norm(z));
    }

    public static double distL1(Complex a,Complex b) {
        Complex z=minus(a,b);
	double t1=Math.abs(z.x);
	double t2=Math.abs(z.y);
	if(t1<t2) return(t2);
	return(t1);
    }


    public double norm() {
        return Math.sqrt(x*x+y*y);
    }

    public Complex unit() {
        double d=norm();
        return new Complex(x/d,y/d);
    }

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


    /**This routine gives a measure of the distance between w and the line segment z1z2*/


   public static double nearness(Complex z1,Complex z2,Complex w) {
 	double d1=dist(z1,z2);
 	double d2=dist(w,z1);
 	double d3=dist(w,z2);
 	double d=(d2+d3)/d1;
 	if(d>1.01) return(100);
 	double a1=area(z1,z2,w);
 	a1=Math.abs(a1);
 	double a2=dist(z1,z2);
 	return(a1/a2);
     }

   public static double area(Complex z1,Complex z2,Complex z3) {
         double a;
         Complex[] z=new Complex[5];
         z[1]=minus(z2,z1);
         z[2]=minus(z3,z1);
         z[3]=conjugate(z[2]);
         z[4]=times(z[1],z[3]);
         a=-z[4].y;
         return(a);
     }


}