# Complex.js - ℂ in JavaSript
[](https://npmjs.org/package/complex.js "View this project on npm")
[](https://travis-ci.org/infusion/Complex.js)
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Complex.js is a well tested JavaScript library to work with complex number arithmetic in JavaScript. It implements every elementary complex number manipulation function and the API is intentionally similar to [Fraction.js](https://github.com/infusion/Fraction.js). Furthermore, it's the basis of [Polynomial.js](https://github.com/infusion/Polynomial.js) and [Math.js](https://github.com/josdejong/mathjs).
Example
===
```js
var Complex = require('complex.js');
var c = new Complex("99.3+8i");
c.mul({re: 3, im: 9}).div(4.9).sub(3, 2);
```
Parser
===
Any function (see below) as well as the constructor of the *Complex* class parses its input like this.
You can pass either Objects, Doubles or Strings.
Objects
---
```javascript
new Complex({re: real, im: imaginary});
new Complex({arg: angle, abs: radius});
new Complex({phi: angle, r: radius});
```
Doubles
---
```javascript
new Complex(55.4);
```
Strings
---
```javascript
new Complex("123.45");
new Complex("15+3i");
new Complex("i");
```
Two arguments
---
```javascript
new Complex(3, 2); // 3+2i
```
Functions
===
Complex sign()
---
Returns the complex sign, defined as the complex number normalized by it's absolute value
Complex add(n)
---
Adds another complex number
Complex sub(n)
---
Subtracts another complex number
Complex mul(n)
---
Multiplies the number with another complex number
Complex div(n)
---
Divides the number by another complex number
Complex pow(exp)
---
Returns the number raised to the complex exponent
Complex sqrt()
---
Returns the complex square root of the number
Complex exp(n)
---
Returns `e^n` with complex exponent `n`.
Complex log()
---
Returns the natural logarithm (base `E`) of the actual complex number
double abs()
---
Calculates the magnitude of the complex number
double arg()
---
Calculates the angle of the complex number
Complex inverse()
---
Calculates the multiplicative inverse of the complex number (1 / z)
Complex conjugate()
---
Calculates the conjugate of the complex number (multiplies the imaginary part with -1)
Complex neg()
---
Negates the number (multiplies both the real and imaginary part with -1) in order to get the additive inverse
Complex floor([places=0])
---
Floors the complex number parts towards zero
Complex ceil([places=0])
---
Ceils the complex number parts off zero
Complex round([places=0])
---
Rounds the complex number parts
boolean equals(n)
---
Checks if both numbers are exactly the same
boolean isNaN()
---
Checks if the given number is not a number
Complex clone()
---
Returns a new Complex instance with the same real and imaginary properties
Array toVector()
---
Returns a Vector of the actual complex number with two components
String toString()
---
Returns a string representation of the actual number. As of v1.9.0 the output is a bit more human readable
```javascript
new Complex(1, 2).toString(); // 1 + 2i
new Complex(0, 1).toString(); // i
new Complex(9, 0).toString(); // 9
new Complex(1, 1).toString(); // 1 + i
```
double valueOf()
---
Returns the real part of the number if imaginary part is zero. Otherwise `null`
Trigonometric functions
===
The following trigonometric functions are defined on Complex.js:
| Trig | Arcus | Hyperbolic | Arcus-Hyperbolic |
|------|-------|------------|------------------|
| sin() | asin() | sinh() | asinh() |
| cos() | acos() | cosh() | acosh() |
| tan() | atan() | tanh() | atanh() |
| cot() | acot() | coth() | acoth() |
| sec() | asec() | sech() | asech() |
| csc() | acsc() | csch() | acsch() |
Constants
===
Complex.ZERO
---
A complex zero instance
Complex.ONE
---
A complex one instance
Complex.I
---
An imaginary number i instance
Complex.PI
---
A complex PI instance
Complex.E
---
A complex euler number instance
Complex.EPSILON
---
A small epsilon value used for `equal()` comparison in order to circumvent double inprecision.
Installation
===
Installing complex.js is as easy as cloning this repo or use one of the following commands:
```
bower install complex.js
```
or
```
npm install complex.js
```
Using Complex.js with the browser
===
Using Complex.js with require.js
===
Coding Style
===
As every library I publish, complex.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.
Testing
===
If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with
```
npm test
```
Copyright and licensing
===
Copyright (c) 2015, Robert Eisele (robert@xarg.org)
Dual licensed under the MIT or GPL Version 2 licenses.