一个复数是一个形式为a+bi的数，这里的a和b都是实数，i是√-1的平方根。数字a和b分别称为复数的实部和虚部。可以使用下面的公式完成复数的加、减、乘、除：
加：a + bi + c + di = (a + c) + (b + d)i
减：a + bi - (c + di) = (a - c) + (b - d)i
乘：(a + bi) * (c + di) = (ac -bd) + (bc + ad)i
除：(a + bi) / (c + di) = (ac + bd)/(c*c + d*d) + (bc - ad)i/(c*c + d*d)
还可以使用下面的公式得到复数的绝对值：
|a + bi| = √(a *a + b*b)
要求：
设计一个名为Complex的复数来表示复数以及完成复数运算的add、substract、multiply、divide和abs方法，并且覆盖toString方法返回一个表示复数的字符串。方法toString返回字符串a + bi。如果b是0，那么它只返回a。Complex类应该也实现Cloneable接口。提供三个构造方法Complex(a,b)、Complex（a）和Complex（）。Complex（）创建数字0的Complex对象，而Complex（a）创建一个b为0的Complex对象。还提供getRealPart()和getImaginaryPart（）方法以分别返回复数的实部和虚部。编写一个测试程序，提示用户输入两个复数，然后显示它们做加、减、乘、除之后的结果。
package pack2;public class Complex implements Cloneable{private double a,b; public Complex() { this(0);}public Complex(double a) {this.a = a;}public Complex(double a, double b) {this.a = a;this.b = b;} //返回复数的加法运算public Complex add(Complex c) {if(c == null) //如果c是null，抛出异常throw new NullPointerException("Invalid Pointer");return new Complex((a + c.a), (b + c.b));} //返回复数的减法运算public Complex substract(Complex c) {if(c == null)throw new NullPointerException("Invalid Pointer");return new Complex((a - c.a), (b - c.b));} //返回复数的乘法运算public Complex multiply(Complex c) {if(c == null)throw new NullPointerException("Invalid Pointer");return new Complex((a * c.a - b * c.b),(a * c.b + b * c.a));} //返回复数的除法运算public Complex divide(Complex c) {if(c == null)throw new NullPointerException("Invalid Pointer");return new Complex((a * c.a + b * c.b) / (Math.pow(c.a, 2) + Math.pow(c.b, 2)),(b * c.a - a * c.b) / (Math.pow(c.a, 2) + Math.pow(c.b, 2)));} //返回复数的绝对值public double abs() {return Math.sqrt(a * a + b *b);}@Overridepublic String toString() {if(Math.abs(b) < 0.00001) //如果b为0，返回a(考虑到浮点数的精度变化，故用Math.abs()方法)return ""+a;elsereturn a+" + "+b+"i";}@Override //重写clone()方法public Object clone(){try {return super.clone(); //调用本地方法返回克隆}catch (CloneNotSupportedException e) {return null;}} //返回实部public double getRealPart() {return a;} //返回虚部public double getImginaryPart() {return b;} //设置实部public void setRealPart(double a) {this.a = a;} //设置虚部public void setImginaryPart(double b) {this.b = b;}}测试程序如下：
package pack2;import java.util.Scanner;public class TestComplex {public static void main(String[] args) {Scanner input = new Scanner(System.in);System.out.print("Enter the first complex number: ");double a = input.nextDouble();double b = input.nextDouble();System.out.print("Enter the second complex number: ");double c = input.nextDouble();double d = input.nextDouble();Complex complex = new Complex(a,b);Complex complex1 = new Complex(c,d);System.out.printf("(%.1f + %.1fi) + (%.1f + %.1fi) = %s ",a,b,c,d,complex.add(complex1));System.out.printf("(%.1f + %.1fi) - (%.1f + %.1fi) = %s ",a,b,c,d,complex.substract(complex1));System.out.printf("(%.1f + %.1fi) * (%.1f + %.1fi) = %s ",a,b,c,d,complex.multiply(complex1));System.out.printf("(%.1f + %.1fi) / (%.1f + %.1fi) = %s ",a,b,c,d,complex.divide(complex1));System.out.printf("|(%.1f + %.1fi)| = %.15f ",a,b,complex.getSoluteValue());input.close();}}