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

public class Renormalize  {

    public static Complex theta(Complex z) {
	double s=Math.sqrt(2)+1;
	Complex a=new Complex(s/2+.5,s/2+.5);
	Complex b=new Complex(0,-3*s-3);
	Complex w=Complex.plus(b,Complex.times(a,z));
	w=w.conjugate();
	return(w);
    }

    public static Complex thetaInverse(Complex z) {
	double s=Math.sqrt(2)+1;
	double x=1/(s+1);
	Complex a=new Complex(x,-x);
	Complex b=new Complex(3,3);
	Complex w=Complex.plus(b,Complex.times(a,z.conjugate()));
	return(w);
    }

    public static Complex rotate(Complex z) {
	double s=Math.sqrt(2)+1;
	Complex a=new Complex(-1,0);
	Complex b=new Complex(6+3/s,3);
	Complex w=Complex.plus(b,Complex.times(a,z));
	return(w);
    }





}