content: /*************************************************************************
   *  Compilation:  javac Complex.java
   *  Execution:    java Complex
   *
   *  Data type for complex numbers.
   *
   *  The data type is "immutable" so once you create and initialize
   *  a Complex object, you cannot change it. The "final" keyword
   *  when declaring re and im enforces this rule, making it a
   *  compile-time error to change the .re or .im fields after
   *  they've been initialized.
   *
   *  % java Complex
   *  a            = 5.0 + 6.0i
   *  b            = -3.0 + 4.0i
   *  Re(a)        = 5.0
   *  Im(a)        = 6.0
   *  b + a        = 2.0 + 10.0i
   *  a - b        = 8.0 + 2.0i
   *  a * b        = -39.0 + 2.0i
   *  b * a        = -39.0 + 2.0i
   *  a / b        = 0.36 - 1.52i
   *  (a / b) * b  = 5.0 + 6.0i
   *  conj(a)      = 5.0 - 6.0i
   *  |a|          = 7.810249675906654
   *  tan(a)       = -6.685231390246571E-6 + 1.0000103108981198i
   *
   *************************************************************************/
  
  public class Complex {
      private final double re;   // the real part
      private final double im;   // the imaginary part
  
      // create a new object with the given real and imaginary parts
      public Complex(double real, double imag) {
          re = real;
          im = imag;
      }
  
      // return a string representation of the invoking Complex object
      public String toString() {
          if (im == 0) return re + "";
          if (re == 0) return im + "i";
          if (im <  0) return re + " - " + (-im) + "i";
          return re + " + " + im + "i";
      }
  
      // return abs/modulus/magnitude and angle/phase/argument
      public double abs()   { return Math.hypot(re, im); }  // Math.sqrt(re*re + im*im)
      public double phase() { return Math.atan2(im, re); }  // between -pi and pi
  
      // return a new Complex object whose value is (this + b)
      public Complex plus(Complex b) {
          Complex a = this;             // invoking object
          double real = a.re + b.re;
          double imag = a.im + b.im;
          return new Complex(real, imag);
      }
  
      // return a new Complex object whose value is (this - b)
      public Complex minus(Complex b) {
          Complex a = this;
          double real = a.re - b.re;
          double imag = a.im - b.im;
          return new Complex(real, imag);
      }
  
      // return a new Complex object whose value is (this * b)
      public Complex times(Complex b) {
          Complex a = this;
          double real = a.re * b.re - a.im * b.im;
          double imag = a.re * b.im + a.im * b.re;
          return new Complex(real, imag);
      }
  
      // scalar multiplication
      // return a new object whose value is (this * alpha)
      public Complex times(double alpha) {
          return new Complex(alpha * re, alpha * im);
      }
  
      // return a new Complex object whose value is the conjugate of this
      public Complex conjugate() {  return new Complex(re, -im); }
  
      // return a new Complex object whose value is the reciprocal of this
      public Complex reciprocal() {
          double scale = re*re + im*im;
          return new Complex(re / scale, -im / scale);
      }
  
      // return the real or imaginary part
      public double re() { return re; }
      public double im() { return im; }
  
      // return a / b
      public Complex divides(Complex b) {
          Complex a = this;
          return a.times(b.reciprocal());
      }
  
      // return a new Complex object whose value is the complex exponential of this
      public Complex exp() {
          return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
      }
  
      // return a new Complex object whose value is the complex sine of this
      public Complex sin() {
          return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
      }
  
      // return a new Complex object whose value is the complex cosine of this
      public Complex cos() {
          return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
      }
  
      // return a new Complex object whose value is the complex tangent of this
      public Complex tan() {
          return sin().divides(cos());
      }
      
  
  
      // a static version of plus
      public static Complex plus(Complex a, Complex b) {
          double real = a.re + b.re;
          double imag = a.im + b.im;
          Complex sum = new Complex(real, imag);
          return sum;
      }
  
  
  
      // sample client for testing
      public static void main(String[] args) {
          Complex a = new Complex(5.0, 6.0);
          Complex b = new Complex(-3.0, 4.0);
  
          StdOut.println("a            = " + a);
          StdOut.println("b            = " + b);
          StdOut.println("Re(a)        = " + a.re());
          StdOut.println("Im(a)        = " + a.im());
          StdOut.println("b + a        = " + b.plus(a));
          StdOut.println("a - b        = " + a.minus(b));
          StdOut.println("a * b        = " + a.times(b));
          StdOut.println("b * a        = " + b.times(a));
          StdOut.println("a / b        = " + a.divides(b));
          StdOut.println("(a / b) * b  = " + a.divides(b).times(b));
          StdOut.println("conj(a)      = " + a.conjugate());
          StdOut.println("|a|          = " + a.abs());
          StdOut.println("tan(a)       = " + a.tan());
      }
  
  }
  