Question

如何获得这个复数的大小（1 + 3J）/（4 + 6J）？我不知道如何以分数形式得到它。

Answer 1

复数的绝对值是其分量之和的平方根，平方。

分部要求：

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

最终，它将像this一样实现，这是我的类的副本来处理这个确切的问题。当然，关于如何实施它的想法存在差异。

/* Copyright (c) 2015 Kevin Wong and Nicholas Colaprete
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
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 * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
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 * Software.
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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));
    }
}

分数中复数的大小

1 个答案: