How to Use Complex Numbers in math.js?

Complex numbers are essential in various fields of science and engineering, particularly in signal processing, quantum mechanics, and control theory. A complex number consists of a real part and an imaginary part, typically written in the form a+bi, where i is the imaginary unit. Math.js, a powerful mathematics library for JavaScript, provides extensive support for complex numbers, allowing you to perform a wide range of operations. In this article, we will explore how to work with complex numbers using math.js.

Setting Up math.js

Before working with complex numbers, you need to set up math.js in your JavaScript environment. You can include math.js in your project by using a CDN or installing it via npm.

Using a CDN

<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/10.0.0/math.js"></script>
<script>
  // Your code here
</script>

Using npm

npm install mathjs

Then, include it in your JavaScript file:

const math = require('mathjs');

Creating Complex Numbers

You can create complex numbers in math.js using the complex function. There are several ways to define a complex number.

Example 1: Creating a Complex Number

const math = require("mathjs");

// Define a complex number
const complexNumber = math.complex(3, 4);

console.log(`The complex number is ${complexNumber}`);

Output:

The complex number is 3 + 4i

Example 2: Creating a Complex Number from a String

const math = require("mathjs");

// Define a complex number from a string
const complexNumber = math.complex("5 + 6i");

console.log(`The complex number is ${complexNumber}`);

Output:

The complex number is 5 + 6i

Basic Operations

Math.js supports basic arithmetic operations with complex numbers, such as addition, subtraction, multiplication, and division.

Example 1: This example demonstrates how to add two complex numbers using the 'mathjs' library in JavaScript.

const math = require("mathjs");

// Define two complex numbers
const z1 = math.complex(2, 3);
const z2 = math.complex(1, 4);

// Add the complex numbers
const sum = math.add(z1, z2);

console.log(`The sum of ${z1} and ${z2} is ${sum}`);

Output:

The sum of 2 + 3i and 1 + 4i is 3 + 7i

Example 2: This example demonstrates how to subtract two complex numbers using the 'mathjs' library in JavaScript.

const math = require('mathjs');

// Define two complex numbers
const z1 = math.complex(5, 7);
const z2 = math.complex(2, 3);

// Subtract the complex numbers
const difference = math.subtract(z1, z2);

console.log(`The difference between ${z1} and ${z2} is ${difference}`); 

Output:

The difference between 5 + 7i and 2 + 3i is 3 + 4i

Example 3: This example demonstrates how to multiply two complex numbers using the 'mathjs' library in JavaScript.

const math = require('mathjs');

// Define two complex numbers
const z1 = math.complex(3, 2);
const z2 = math.complex(1, 4);

// Multiply the complex numbers
const product = math.multiply(z1, z2);

console.log(`The product of ${z1} and ${z2} is ${product}`);

Output:

 The product of 3 + 2i and 1 + 4i is -5 + 14i

Example 4: This example demonstrates how to divide two complex numbers using the 'mathjs' library in JavaScript.

const math = require('mathjs');

// Define two complex numbers
const z1 = math.complex(7, 6);
const z2 = math.complex(3, 2);

// Divide the complex numbers
const quotient = math.divide(z1, z2);

console.log(`The quotient of ${z1} divided by ${z2} is ${quotient}`);

Output:

The quotient of 7 + 6i divided by 3 + 2i is 2.5384615384615388 + 0.3076923076923079i