复数的加减乘除JAVA

在Java中处理复数（Complex numbers），通常我们会创建一个名为`Complex`的类来封装实部（real part）和虚部（imaginary part）。复数的加减乘除操作可以按照数学规则来实现：

1. **构造函数**：用于初始化复数的值，如`Complex(double real, double imaginary)`。

public class Complex {
    private double real;
    private double imaginary;

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

2. **加法（Addition）**：两个复数相加，实部加实部，虚部加虚部。

public Complex add(Complex other) {
    double sumReal = real + other.real;
    double sumImaginary = imaginary + other.imaginary;
    return new Complex(sumReal, sumImaginary);
}

3. **减法（Subtraction）**：类似于加法，只是方向相反。

public Complex subtract(Complex other) {
    double diffReal = real - other.real;
    double diffImaginary = imaginary - other.imaginary;
    return new Complex(diffReal, diffImaginary);
}

4. **乘法（Multiplication）**：涉及到分配律和i^2 = -1的特性。

public Complex multiply(Complex other) {
    double productReal = real * other.real - imaginary * other.imaginary;
    double productImaginary = real * other.imaginary + imaginary * other.real;
    return new Complex(productReal, productImaginary);
}

5. **除法（Division）**：更复杂一些，需要将除数转换为极坐标形式，并做相应计算。

public Complex divide(Complex divisor) {
    double denominatorSquare = divisor.real * divisor.real + divisor.imaginary * divisor.imaginary;
    double quotientReal = (real * divisor.real + imaginary * divisor.imaginary) / denominatorSquare;
    double quotientImaginary = (imaginary * divisor.real - real * divisor.imaginary) / denominatorSquare;
    // 如果分母为零，抛出异常
    if (denominatorSquare == 0) throw new ArithmeticException("Cannot divide by zero");
    return new Complex(quotientReal, quotientImaginary);
}