Complex Numbers in PHP

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)