分数の複素数の大きさ

Question

この複素数の大きさを得る方法 （1 + 3j）/（4 + 6j）？ 分数形式で取得する方法がわかりません。

Answer 1

複素数の絶対値は、コンポーネントの合計の平方根です。

部門は、その本が必要です。

最後に、この正確な問題に対処するために私のクラスのコピーである this、のように実装されるだろう、

http://www.mesacc.edu/~scotz47781/mat120/notes/complex/dividing/dividing_complex.html

。もちろん、それを実装する方法にはアイデアに違いがあります。

/* Copyright (c) 2015 Kevin Wong and Nicholas Colaprete 
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* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR 
* OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ 

package javapy.maths; 

/** 
* The Complex class represents complex numbers. Complex instances are constant; their values cannot be changed after 
* they are created and are hence, immutable. 
* 
* @author ncolaprete 
* @author ifly6 
*/ 
public class Complex { 

    private final double real; 
    private final double imaginary; 

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

    /** 
    * Returns a string representation of the object in the form <code>a + b<i>i</i></code>. 
    * 
    * @return the string representation 
    */ 
    @Override public String toString() { 
     if (this.imaginary == 0) { 
      return Double.toString(this.real); 
     } else { 
      if (this.real == 0) { return this.imaginary + "i"; } 
      return this.real + "+" + this.imaginary + "i"; 
     } 
    } 

    /** 
    * Returns a double array containing the real part under index 0 and the imaginary part under index 1. 
    * 
    * @return An array representation of the number in the form <code>{ real, imaginary }</code> 
    */ 
    public double[] toArray() { 
     return new double[] { this.real, this.imaginary }; 
    } 

    /** 
    * Adds this complex number to another one. 
    * 
    * @param num - Complex number to add to. 
    * @return new <code>Complex</code> which is the sum of the two numbers. 
    */ 
    public Complex add(Complex num) { 
     double realfinal = this.real + num.real; 
     double imagfinal = this.imaginary + num.imaginary; 
     return new Complex(realfinal, imagfinal); 
    } 

    /** 
    * Subtracts this complex number by another one. 
    * 
    * @param num - Complex number to subtract from. 
    * @return new <code>Complex</code> which is the difference of the two numbers. 
    */ 
    public Complex subtract(Complex num) { 
     double realfinal = this.real - num.real; 
     double imagfinal = this.imaginary - num.imaginary; 
     return new Complex(realfinal, imagfinal); 
    } 

    /** 
    * Multiplies this complex number by another one. 
    * 
    * @param num - Complex number to multiply with. 
    * @return new <code>Complex</code> which is the product of the two numbers. 
    */ 
    public Complex multiply(Complex num) { 
     double re = this.real * num.real; 
     double im = (this.imaginary * num.real) + (num.imaginary * this.real); 
     double imSqrd = (this.imaginary * num.imaginary) * (-1); 
     return new Complex(re + imSqrd, im); 
    } 

    /** 
    * Divides this complex number by another one. If it cannot be divided for some reason, then it will return 
    * <code>null</code>. 
    * 
    * @param num - Complex number to divide by. 
    * @return new <code>Complex</code> which is the quotient of the two numbers. 
    */ 
    public Complex divide(Complex num) { 
     Complex top = this.multiply(num.conjugate()); 
     Complex bottom = num.multiply(num.conjugate()); 

     if (bottom.imaginary == 0) { 
      return new Complex(top.real/bottom.real, top.imaginary/bottom.real); 
     } else { 
      return null; 
     } 
    } 

    /** 
    * Returns the conjugate of the Complex number. 
    * 
    * @return the conjugate 
    */ 
    public Complex conjugate() { 
     return new Complex(real, -imaginary); 
    } 

    /** 
    * Returns this complex number raised to an integer power. 
    * 
    * @param power to raise to 
    * @return the number raised to the given power 
    */ 
    public Complex raisedTo(int power) { 
     Complex to_sender = this; 
     for (int i = 0; i < power; i++) { 
      to_sender = to_sender.multiply(to_sender); 
     } 
     return to_sender; 
    } 

    /** 
    * Returns the absolute magnitude of complex number on the imaginary plane. 
    * 
    * @return absolute magnitude, as double 
    */ 
    public double magnitude() { 
     return Math.sqrt(Math.pow(this.real, 2) + Math.pow(this.imaginary, 2)); 
    } 
}