用java Complex复数类声明实现Comparable<T>接口，提供按模比较复数大小的方法

好的，以下是用Java中的Complex复数类声明实现Comparable<T>接口，提供按模比较复数大小的方法的代码：

import java.util.*;

public class Complex implements Comparable<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);
    }

    // return a new object whose value is (this * alpha)
    public Complex scale(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());
    }

    // comparison by modulus
    public int compareTo(Complex other) {
        if (this.abs() < other.abs()) {
            return -1;
        } else if (this.abs() > other.abs()) {
            return 1;
        } else {
            return 0;
        }
    }

    // test client
    public static void main(String[] args) {
        Complex z1 = new Complex(1.0, 1.0);
        Complex z2 = new Complex(2.0, 2.0);

        System.out.println(z1.compareTo(z2)); // prints -1

        Complex[] arr = {new Complex(3.0, 3.0), new Complex(1.0, 1.0), new Complex(2.0, 2.0)};
        Arrays.sort(arr);

        for (Complex c : arr) {
            System.out.println(c);
        }

        // prints 1.0 + 1.0i
        //        2.0 + 2.0i
        //        3.0 + 3.0i
    }
}

在上述代码中，我们实现了`Comparable<Complex>`接口，并提供了`compareTo()`方法，该方法按照复数的模进行比较，并返回-1、0或1，以表示当前对象小于、等于或大于另一个对象。我们使用`Arrays.sort()`方法对一个复数数组进行排序，以演示这个方法的工作原理。