Complex.java

public class Complex
{
  private final double re;
  private final double im;

  public Complex(double real, double imag)
  {re = real; im = imag;  }

  public Complex plus(Complex b)
  {  //return the sum of this number and b
     double real = re + b.re;
     double imag = im + b.im;
     return new Complex(real, imag);
  }

   public Complex minus(Complex b)
  {  //return the sum of this number and b
     double real = re - b.re;
     double imag = im - b.im;
     return new Complex(real, imag);
  }

  public Complex times(Complex b)
  {  //return the product of this number and b
     double real = re * b.re - im * b.im;
     double imag = re * b.im + im * b.re; 
     return new Complex(real, imag);
  }

  public Complex reciprocal() 
  {
      double scale = re*re + im*im;
      return new Complex(re / scale, -im / scale);
  }

  public Complex division(Complex b) 
  {
      return this.times(b.reciprocal());
  }

  public double abs()
  { return Math.sqrt(re*re +im*im);}

  public double re()
  {return re; }

  public double im()
  {return im; }

  public String toString()
  {
    return re + " + " + im + "i";
  }

  public static void main(String[] args)
  {
    Complex z0 = new Complex(1.0, 1.0);
    Complex z = z0;
    z = z.times(z).plus(z0);
    z = z.times(z).plus(z0);
    System.out.println(z);
  }
}