Complex Numbers in PHP - Coding

In the mathematical computations, complex numbers play a crucial role, especially in fields like engineering and physics. A complex number is a combination of a real part and an imaginary part, often expressed as a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit. In this article, we will explore PHP for handling complex numbers.

Basic Complex Number Class

Let’s start by creating a basic PHP class to represent complex numbers. This class will include methods for addition, subtraction, multiplication, and string representation of complex numbers.

Example:

PHP

<?php 
  
class ComplexNumber { 
    private $real; 
    private $imaginary; 
  
    public function __construct($real, $imaginary) { 
        $this->real = $real; 
        $this->imaginary = $imaginary; 
    } 
  
    public function add(ComplexNumber $complexNumber) { 
        return new ComplexNumber( 
            $this->real + $complexNumber->getReal(), 
            $this->imaginary + $complexNumber->getImaginary() 
        ); 
    } 
  
    public function subtract(ComplexNumber $complexNumber) { 
        return new ComplexNumber( 
            $this->real - $complexNumber->getReal(), 
            $this->imaginary - $complexNumber->getImaginary() 
        ); 
    } 
  
    public function multiply(ComplexNumber $complexNumber) { 
        $real = $this->real * $complexNumber->getReal()  
            - $this->imaginary * $complexNumber->getImaginary(); 
              
        $imaginary = $this->real * $complexNumber->getImaginary()  
            + $this->imaginary * $complexNumber->getReal(); 
              
        return new ComplexNumber($real, $imaginary); 
    } 
  
    public function __toString() { 
        return "({$this->real}, {$this->imaginary}i)"; 
    } 
  
    public function getReal() { 
        return $this->real; 
    } 
  
    public function getImaginary() { 
        return $this->imaginary; 
    } 
} 
  
// Driver code 
$complex1 = new ComplexNumber(2, 3); 
$complex2 = new ComplexNumber(1, -2); 
  
$sum = $complex1->add($complex2); 
$difference = $complex1->subtract($complex2); 
$product = $complex1->multiply($complex2); 
  
echo "Sum: $sum, Difference: $difference, Product: $product"; 
  
?>

Output

Sum: (3, 1i), Difference: (1, 5i), Product: (8, -1i)

Additional Operations

In more advanced use cases, you might want to implement additional operations such as division, magnitude calculation, and conjugate.

Example:

PHP

<?php 
  
class ComplexNumber { 
    private $real; 
    private $imaginary; 
  
    public function __construct($real, $imaginary) { 
        $this->real = $real; 
        $this->imaginary = $imaginary; 
    } 
  
    public function divide(ComplexNumber $complexNumber) { 
        $denominator = $complexNumber->getReal()**2  
            + $complexNumber->getImaginary()**2; 
              
        $real = ($this->real * $complexNumber->getReal()  
            + $this->imaginary * $complexNumber->getImaginary())  
            / $denominator; 
              
        $imaginary = ($this->imaginary * $complexNumber->getReal()  
            - $this->real * $complexNumber->getImaginary())  
            / $denominator; 
              
        return new ComplexNumber($real, $imaginary); 
    } 
  
    public function magnitude() { 
        return sqrt($this->real**2 + $this->imaginary**2); 
    } 
  
    public function conjugate() { 
        return new ComplexNumber($this->real, -$this->imaginary); 
    } 
      
    public function __toString() { 
        return "({$this->real}, {$this->imaginary}i)"; 
    } 
  
    public function getReal() { 
        return $this->real; 
    } 
  
    public function getImaginary() { 
        return $this->imaginary; 
    } 
} 
  
// Driver code 
$complex1 = new ComplexNumber(2, 3); 
$complex2 = new ComplexNumber(1, -2); 
  
$quotient = $complex1->divide($complex2); 
$magnitude = $complex1->magnitude(); 
$conjugate = $complex1->conjugate(); 
  
echo "Quotient: $quotient, Magnitude: $magnitude, Conjugate: $conjugate"; 
  
?>

Output

Quotient: (-0.8, 1.4i), Magnitude: 3.605551275464, Conjugate: (2, -3i)

Reffered: https://www.geeksforgeeks.org

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