Complex Numbers in JavaScript

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Complex numbers are often used in mathematics, engineering, and physics. But, JavaScript doesn't have built-in support for complex numbers. Don't let that discourage you, though! In this article, we'll explore how to create a custom Complex class to represent complex numbers and perform mathematical operations with them.

Complex Number Basics

A complex number is a number with a real part and an imaginary part. It's usually written in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, which is the square root of -1.

To get started, let's create a Complex class to represent complex numbers in JavaScript.

class Complex {
    constructor(real, imaginary) {
        this.real = real;
        this.imaginary = imaginary;
    }
}

Now, we've got a basic Complex class that can hold a complex number's real and imaginary parts. But that's just the beginning! Let's add some methods to perform mathematical operations on our complex numbers.

Addition

To add two complex numbers, simply add their corresponding real parts and imaginary parts. Here's how to do it:

class Complex {
    // ... constructor and other code

    add(complex) {
        return new Complex(this.real + complex.real, this.imaginary + complex.imaginary);
    }
}

Subtraction

Subtracting complex numbers is similar to addition. Just subtract the corresponding real and imaginary parts:

class Complex {
    // ... constructor and other code

    subtract(complex) {
        return new Complex(this.real - complex.real, this.imaginary - complex.imaginary);
    }
}

Multiplication

Multiplying complex numbers involves some more arithmetic. To multiply two complex numbers (a + bi) and (c + di), you can use the following formula:

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Here's how to implement multiplication in the Complex class:

class Complex {
    // ... constructor and other code

    multiply(complex) {
        const real = this.real * complex.real - this.imaginary * complex.imaginary;
        const imaginary = this.real * complex.imaginary + this.imaginary * complex.real;
        return new Complex(real, imaginary);
    }
}

Division

Division is a bit more complicated. To divide two complex numbers (a + bi) and (c + di), you can use the following formula:

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

Here's the implementation for the Complex class:

class Complex {
    // ... constructor and other code

    divide(complex) {
        const denominator = complex.real ** 2 + complex.imaginary ** 2;
        const real = (this.real * complex.real + this.imaginary * complex.imaginary) / denominator;
        const imaginary = (this.imaginary * complex.real - this.real * complex.imaginary) / denominator;
        return new Complex(real, imaginary);
    }
}

Putting It All Together

Now, we've implemented a Complex class that can handle basic arithmetic operations with complex numbers. Here's the complete class for reference:

class Complex {
    constructor(real, imaginary) {
        this.real = real;
        this.imaginary = imaginary;
    }

    add(complex) {
        return new Complex(this.real + complex.real, this.imaginary + complex.imaginary);
    }

    subtract(complex) {
        return new Complex(this.real - complex.real, this.imaginary - complex.imaginary);
    }

    multiply(complex) {
        const real = this.real * complex.real - this.imaginary * complex.imaginary;
        const imaginary = this.real * complex.imaginary + this.imaginary * complex.real;
        return new Complex(real, imaginary);
    }

    divide(complex) {
        const denominator = complex.real ** 2 + complex.imaginary ** 2;
        const real = (this.real * complex.real + this.imaginary * complex.imaginary) / denominator;
        const imaginary = (this.imaginary * complex.real - this.real * complex.imaginary) / denominator;
        return new Complex(real, imaginary);
    }
}

With this custom Complex class, you can now work with complex numbers in JavaScript with ease. Happy coding!

FAQ

class Complex {
    constructor(real, imaginary) {
        this.real = real;
        this.imaginary = imaginary;
    }
}

let complexNumber = new Complex(3, 4);

class Complex {
    // ...constructor...
    add(other) {
        return new Complex(this.real + other.real, this.imaginary + other.imaginary);
    }
}

class Complex {
    // ...constructor and other methods...
    magnitude() {
        return Math.sqrt(this.real * this.real + this.imaginary * this.imaginary);
    }
    argument() {
        return Math.atan2(this.imaginary, this.real);
    }
}

class Complex {
    // ...constructor and other methods...
    conjugate() {
        return new Complex(this.real, -this.imaginary);
    }
}

let complexNumber = new Complex(3, 4);
let conjugateNumber = complexNumber.conjugate();