复数的四则运算（java版）

介绍

复数，为实数的延伸，它使任一多项式方程都有根。复数当中有个“虚数单位 ” i，它是−1的一个平方根，即 i^2=−1。任一复数都可表达为 **x+yi，**其中x及y皆为实数，分别称为复数之“实部”和“虚部”。

四则运算，是一种简单基本的数学运算，即加法、减法、乘法和除法四种运算。

复数的四则运算

要想实现复数的四则运算，我们就要先知道复数的四则运算分别都是如何计算的。

两个复数的四则运算（数学表达式）

复数一：a+bi  
复数二：c+di加法 a+bi + c+di = (a+c)+(b+d)i
减法 a+bi - (c+di) = (a-c)+(b+d)i
乘法 a+bi * (c+di) = (ac-bd) + (ad+bc)i
除法 (a+bi)/(c+di) = [(ac+bd)+(bc-ad)i]/(c^2+d^2)

实现思路

由于 java程序设计语言是一门面向对象编程的，所以我们可以考虑把复数封装成一个类，然后我们就可以实例化这个类，创建复数对象。我们在封装这个类的时候就可以思考该怎么封装，要去思考复数这个对象中应该具备什么样的属性和特征。

状态特征

状态特征也就是复数对象拥有的属性，应该有实部和虚部

行为特征

行为特征也就是复数对象的具备方法，除了构造和setter and getter 方法，还应该有实现复数相加的方法add()，实现复数相减的方法sub(),实现复数相乘的方法mul(),实现复数相除的除法div()，还有重写toString()的方法。

代码

1、封装复数类

//复数的四则运算
public class Complex {//实部和虚部的定义//定义成double比较好的的原因之一是因为 有除法运算private double realPart;private double imagePart;//构造方法public Complex() {}public Complex(double realPart, double imagePart) {this.realPart = realPart;this.imagePart = imagePart;}//setter and getterpublic double getImagePart() {return imagePart;}public void setImagePart(double imagePart) {this.imagePart = imagePart;}public double getRealPart() {return realPart;}public void setRealPart(double realPart) {this.realPart = realPart;}//复数的加法public Complex add(Complex complexNumber) {if (complexNumber == null) {System.out.println("复数对象输入错误");return new Complex();}double newImagePart = this.getImagePart() + complexNumber.getImagePart();double newRealPart = this.getRealPart() + complexNumber.getRealPart();return new Complex(newRealPart, newImagePart);}//复数的减法public Complex sub(Complex complexNumber) {if (complexNumber == null) {System.out.println("复数对象输入错误");return new Complex();}double newImagePart = this.getImagePart() - complexNumber.getImagePart();double newRealPart = this.getRealPart() - complexNumber.getRealPart();return new Complex(newRealPart, newImagePart);}//复数的乘法public Complex mul(Complex complexNumber) {if (complexNumber == null) {System.out.println("输入复数对象错误");return new Complex();}double newRealPart = this.getRealPart() * complexNumber.getRealPart() - this.getImagePart() * complexNumber.getImagePart();double newImagePart = this.getRealPart() * complexNumber.getImagePart() + this.getImagePart() * complexNumber.getRealPart();return new Complex(newRealPart, newImagePart);}public Complex division(Complex complexNumber) {if (complexNumber == null) {System.out.println("输入复数对象错误");return new Complex();}double newRealPart = (this.getRealPart() * complexNumber.getRealPart() + this.getImagePart() * complexNumber.getImagePart()) / (complexNumber.getRealPart() * complexNumber.getRealPart() + complexNumber.getImagePart() * complexNumber.getImagePart());double newImagePart = (-this.getRealPart() * complexNumber.getImagePart() + this.getImagePart() * complexNumber.getRealPart())/ (complexNumber.getRealPart() * complexNumber.getRealPart() + complexNumber.getImagePart() * complexNumber.getImagePart());return new Complex(newRealPart, newImagePart);}//重写toString方法public String toString(){if(this.imagePart>0){return this.realPart+"+"+this.imagePart+"i"; //如果是虚部是正数，需要手动添加 +}else if(this.imagePart<0){return this.realPart+this.imagePart+"i";//如果虚部是负数，不用给你手动添加 -（运算的结果自带）}else return this.realPart+" ";}}

2、测试复数类

import java.util.Scanner;//测试封装的复数类，实现负数的四则运算
public class ComplexTest {//这里我们可以采取从键盘中输入复数的实部和虚部public static void main(String[] args) {double realPart ;double imagePart ;Scanner s = new Scanner(System.in);System.out.print("输入第一个复数的实部：");realPart = s.nextDouble();System.out.print("输入第一个复数的虚部：");imagePart = s.nextDouble();Complex complex1 = new Complex(realPart,imagePart);System.out.print("输入第二个复数的实部：");realPart = s.nextDouble();System.out.print("输入第二个复数的虚部：");imagePart = s.nextDouble();Complex complex2 = new Complex(realPart,imagePart);//测试复数的加减乘除System.out.println("加法："+ complex1.add(complex2));System.out.println("减法："+complex1.sub(complex2));System.out.println("乘法："+complex1.mul(complex2));System.out.println("除法："+complex1.division(complex2));}
}