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/*************************************************************************

* 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());

}