复数类及各种操作（Java）

package fft; import fft.*;/************************************************************************* *  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)     *          减法     * @param b     * @return     */    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)     *    乘以一个复数     * @param b  被乘的复数     * @return     */    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)</br>     *                乘以一个实数     */    public Complex times(double alpha) {        return new Complex(alpha * re, alpha * im);    }    /**     *  return a new Complex object whose value is the conjugate of this</br>     *   共轭复数     * @return     */    public Complex conjugate() {  return new Complex(re, -im); }    /**     *  return a new Complex object whose value is the reciprocal of this</br>     *     倒数 a +bi 的倒数  </br>     *   a -bi</br>     * —————————————</br>     *   a^2  + b ^2</br>     */       public Complex reciprocal()    {    double scale = re*re + im*im;        return new Complex(re / scale, -im / scale);    }    /**     *  return the real part     * @return     */    public double re() { return re; }    /**     *  imaginary part     * @return     */    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());        System.out.println("tan(a)       = " + a.tan());    }}