Answer to Question #279547 in Java | JSP | JSF for Chandresn

Question

A complex number is a number in the form a+bi, where a and b are real numbers and i is

(square root of -1).

The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas:

a+bi+c+di = (a + c) + (b+d)i

a+bi (c+di) = (ac) + (b-d)i

(a + bi)*(c+di) = (ac-bd) + (bc + ad)i (a + bi)/(c+di) = (ac+bd)/(c² +d²) + (bc-ad)i/(c² +d²)

You can also obtain the absolute value for a complex number using the following formula:

|a + bil= √a² + b²

(A complex number can be interpreted as a point on a plane by identifying the (a,b) values as the coordinates of the point. The absolute value of the complex number corresponds to the distance of the point to the origin)

Design a class named Complex for representing complex numbers and the methods add, subtract,

multiply, divide, and abs for performing complex-number operations, and override toStrin

Answer 1

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

  public double getReal() { return real; }
  public double getImaginary() { return imaginary; }

  public static Complex add(final Complex lhs, final Complex rhs) {
    return new Complex(lhs.real + rhs.real, lhs.imaginary + rhs.imaginary);
  } 
  public static Complex subtract(final Complex lhs, final Complex rhs) {
    return new Complex(lhs.real - rhs.real, lhs.imaginary - rhs.imaginary);
  }
  public static Complex multiply(final Complex lhs, final Complex rhs) {
    return new Complex((lhs.real * rhs.real - lhs.imaginary * rhs.imaginary), 
                  (lhs.real * rhs.imaginary + lhs.imaginary * rhs.real));
  }
  public static Complex divide(final Complex lhs, final Complex rhs) {
      double dominator = rhs.real * rhs.real + rhs.imaginary * rhs.imaginary;
    return new Complex((lhs.real * rhs.real + lhs.imaginary * rhs.imaginary) / dominator,
                  (lhs.real * rhs.imaginary + lhs.imaginary * rhs.real) / dominator);
  }
  public static double abs(final Complex complex) {
    return Math.sqrt(complex.real * complex.real + complex.imaginary * complex.imaginary);
  }
  @Override
  public String toString() { 
    return String.format("( %.2f ) + ( %.2f ) i", real, imaginary);
  }
}