/*************************************************************************
 * From: http://introcs.cs.princeton.edu/java/home/ (Section 9.7)
 *
 * 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);

 System.out.println("a = " + a);
 System.out.println("b = " + b);
 System.out.println("Re(a) = " + a.re());
 System.out.println("Im(a) = " + a.im());
 System.out.println("b + a = " + b.plus(a));
 System.out.println("a - b = " + a.minus(b));
 System.out.println("a * b = " + a.times(b));
 System.out.println("b * a = " + b.times(a));
 System.out.println("a / b = " + a.divides(b));
 System.out.println("(a / b) * b = " + a.divides(b).times(b));
 System.out.println("conj(a) = " + a.conjugate());
 System.out.println("|a| = " + a.abs());
 }

}