// This example is from _Java Examples in a Nutshell_. (http://www.oreilly.com)
// Copyright (c) 1997 by David Flanagan
// This example is provided WITHOUT ANY WARRANTY either expressed or implied.
// You may study, use, modify, and distribute it for non-commercial purposes.
// For any commercial use, see http://www.davidflanagan.com/javaexamples

/**
 * This class represents complex numbers, and defines methods for performing
 * arithmetic on complex numbers.
 **/
public class ComplexNumber {
  // These are the instance variables.  Each ComplexNumber object holds
  // two double values, known as x and y.  They are private, so they are
  // not accessible from outside this class.  Instead, they are available 
  // through the real() and imaginary() methods below.
  private double x, y;

  /** This is the constructor.  It initializes the x and y variables */
  public ComplexNumber(double real, double imaginary) {
    this.x = real;
    this.y = imaginary;
  }

  /** 
   * An accessor method.  Returns the real part of the complex number.
   * Note that there is no setReal() method to set the real part.  This means
   * that the ComplexNumber class is "immutable".
   **/
  public double real() { return x; }

  /** An accessor method.  Returns the imaginary part of the complex number */
  public double imaginary() { return y; }

  /** Compute the magnitude of a complex number */
  public double magnitude() { return Math.sqrt(x*x + y*y); }

  /** 
   * This method converts a ComplexNumber to a string.  This is a method of
   * Object that we override so that complex numbers can be meaningfully
   * converted to strings, and so they can conveniently be printed out with
   * System.out.println() and related methods
   **/
  public String toString() { return "{" + x + "," + y + "}"; }

  /** 
   * This is a static class method.  It takes two complex numbers, adds them, 
   * and returns the result as a third number.  Because it is static, there is
   * no "current instance" or "this" object.  Use it like this:
   * ComplexNumber c = ComplexNumber.add(a, b);
   **/
  public static ComplexNumber add(ComplexNumber a, ComplexNumber b) {
    return new ComplexNumber(a.x + b.x, a.y + b.y);
  }

  /**
   * This is a non-static instance method by the same name.  It adds the
   * specified complex number to the current complex number.  Use it like this:
   * ComplexNumber c = a.add(b);
   **/
  public ComplexNumber add(ComplexNumber a) {
    return new ComplexNumber(this.x + a.x, this.y+a.y);
  }

  /** A static class method to multiply complex numbers */
  public static ComplexNumber multiply(ComplexNumber a, ComplexNumber b) {
    return new ComplexNumber(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
  }

  /** An instance method to multiply complex numbers */
  public ComplexNumber multiply(ComplexNumber a) {
    return new ComplexNumber(x*a.x - y*a.y, x*a.y + y*a.x);
  }
}