高數 複數的四則運算

1、代碼。

package com.zxj.reptile.utils.number;

public class Complex {
    private double real;//實數
    private double image;//虛數

    public Complex() {
        real = 0;
        image = 0;
    }

    public Complex(double real, double image) {
        this.real = real;
        this.image = image;
    }

    //加：(a+bi)+(c+di)=(a+c)+(b+d)i
    public Complex add(Complex complex) {
        double real = complex.getReal();
        double image = complex.getImage();
        double newReal = this.real + real;
        double newImage = this.image + image;
        return new Complex(newReal, newImage);
    }

    //減：(a+bi)-(c+di)=(a-c)+(b-d)i
    public Complex sub(Complex complex) {
        double real = complex.getReal();
        double image = complex.getImage();
        double newReal = this.real - real;
        double newImage = this.image - image;
        return new Complex(newReal, newImage);
    }

    //乘：(a+bi)(c+di)=(ac-bd)+(bc+ad)i
    public Complex mul(Complex complex) {
        double real = complex.getReal();
        double image = complex.getImage();
        double newReal = this.real * real - this.image * image;
        double newImage = this.image * real + this.real * image;
        return new Complex(newReal, newImage);
    }

    //乘：a(c+di)=ac+adi
    public Complex mul(double multiplier) {
        return mul(new Complex(multiplier, 0));
    }

    //除：(a+bi)/(c+di)=(ac+bd)/(c^2+d^2) +((bc-ad)/(c^2+d^2))i
    public Complex div(Complex complex) {
        double real = complex.getReal();
        double image = complex.getImage();
        double denominator = real * real + image * image;
        double newReal = (this.real * real + this.image * image) / denominator;
        double newImage = (this.image * real - this.real * image) / denominator;
        return new Complex(newReal, newImage);
    }

    //歐拉公式 e^(ix)=cosx+isinx
    public static Complex euler(double x) {
        double newReal = Math.cos(x);
        double newImage = Math.sin(x);
        return new Complex(newReal, newImage);
    }

    public double getReal() {
        return real;
    }

    public void setReal(double real) {
        this.real = real;
    }

    public double getImage() {
        return image;
    }

    public void setImage(double image) {
        this.image = image;
    }

    @Override
    public String toString() {
        String str = "";
        if (real != 0) {
            str += real;
        } else {
            str += "0";
        }
        if (image < 0) {
            str += image + "i";
        } else if (image > 0) {
            str += "+" + image + "i";
        }
        return str;
    }
}

2、複數四則運算的例子。

package com.zxj.reptile.test.number;

import com.zxj.reptile.utils.number.Complex;

public class ComplexTest {
    public static void main(String[] args) {
        Complex ab = new Complex(2, 3);
        Complex cd = new Complex(5, -4);
        double multiplier = -1;

        System.out.println("複數四則運算的例子：");
        System.out.println(String.format("加發： (%s) + (%s) = (%s)", ab, cd, ab.add(cd)));
        System.out.println(String.format("減法： (%s) - (%s) = (%s)", ab, cd, ab.sub(cd)));
        System.out.println(String.format("乘法： (%s) * (%s) = (%s)", ab, cd, ab.mul(cd)));
        System.out.println(String.format("乘法： (%s) * (%f) = (%s)", ab, multiplier, ab.mul(multiplier)));
        System.out.println(String.format("除法： (%s) / (%s) = (%s)", ab, cd, ab.div(cd)));
    }
}

3、結果。