Below is the syntax highlighted version of Complex.java
from §9.9 Scientific Computing.
/****************************************************************************** * Compilation: javac Complex.java * Execution: java Complex * Dependencies: StdOut.java * * 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 * ******************************************************************************/ /** * The {@code Complex} class represents a complex number. * Complex numbers are immutable: their values cannot be changed after they * are created. * It includes methods for addition, subtraction, multiplication, division, * conjugation, and other common functions on complex numbers. * <p> * This computes correct results if all arithmetic performed is * without floating-point rounding error or arithmetic overflow. * In practice, there will be floating-point rounding error. * <p> * For additional documentation, see <a href="https://algs4.cs.princeton.edu/99scientific">Section 9.9</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */ public class Complex { private final double re; // the real part private final double im; // the imaginary part /** * Initializes a complex number from the specified real and imaginary parts. * * @param real the real part * @param imag the imaginary part */ public Complex(double real, double imag) { re = real; im = imag; } /** * Returns a string representation of this complex number. * * @return a string representation of this complex number, * of the form 34 - 56i. */ 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"; } /** * Returns the absolute value of this complex number. * This quantity is also known as the <em>modulus</em> or <em>magnitude</em>. * * @return the absolute value of this complex number */ public double abs() { return Math.hypot(re, im); } /** * Returns the phase of this complex number. * This quantity is also known as the <em>angle</em> or <em>argument</em>. * * @return the phase of this complex number, a real number between -pi and pi */ public double phase() { return Math.atan2(im, re); } /** * Returns the sum of this complex number and the specified complex number. * * @param that the other complex number * @return the complex number whose value is {@code (this + that)} */ public Complex plus(Complex that) { double real = this.re + that.re; double imag = this.im + that.im; return new Complex(real, imag); } /** * Returns the result of subtracting the specified complex number from * this complex number. * * @param that the other complex number * @return the complex number whose value is {@code (this - that)} */ public Complex minus(Complex that) { double real = this.re - that.re; double imag = this.im - that.im; return new Complex(real, imag); } /** * Returns the product of this complex number and the specified complex number. * * @param that the other complex number * @return the complex number whose value is {@code (this * that)} */ public Complex times(Complex that) { double real = this.re * that.re - this.im * that.im; double imag = this.re * that.im + this.im * that.re; return new Complex(real, imag); } /** * Returns the product of this complex number and the specified scalar. * * @param alpha the scalar * @return the complex number whose value is {@code (alpha * this)} */ public Complex scale(double alpha) { return new Complex(alpha * re, alpha * im); } /** * Returns the product of this complex number and the specified scalar. * * @param alpha the scalar * @return the complex number whose value is {@code (alpha * this)} * @deprecated Replaced by {@link #scale(double)}. */ @Deprecated public Complex times(double alpha) { return new Complex(alpha * re, alpha * im); } /** * Returns the complex conjugate of this complex number. * * @return the complex conjugate of this complex number */ public Complex conjugate() { return new Complex(re, -im); } /** * Returns the reciprocal of this complex number. * * @return the complex number whose value is {@code (1 / this)} */ public Complex reciprocal() { double scale = re*re + im*im; return new Complex(re / scale, -im / scale); } /** * Returns the real part of this complex number. * * @return the real part of this complex number */ public double re() { return re; } /** * Returns the imaginary part of this complex number. * * @return the imaginary part of this complex number */ public double im() { return im; } /** * Returns the result of dividing the specified complex number into * this complex number. * * @param that the other complex number * @return the complex number whose value is {@code (this / that)} */ public Complex divides(Complex that) { return this.times(that.reciprocal()); } /** * Returns the complex exponential of this complex number. * * @return the complex exponential of this complex number */ public Complex exp() { return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im)); } /** * Returns the complex sine of this complex number. * * @return the complex sine of this complex number */ public Complex sin() { return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im)); } /** * Returns the complex cosine of this complex number. * * @return the complex cosine of this complex number */ public Complex cos() { return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im)); } /** * Returns the complex tangent of this complex number. * * @return the complex tangent of this complex number */ public Complex tan() { return sin().divides(cos()); } /** * Unit tests the {@code Complex} data type. * * @param args the command-line arguments */ 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()); } }