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# Complex.js - ℂ in JavaSript
[](https://npmjs.org/package/complex.js)
[](https://travis-ci.org/infusion/Complex.js)
[](http://opensource.org/licenses/MIT)
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});
new Complex([real, imaginary]); // Vector/Array syntax
```
If there are other attributes on the passed object, they're not getting preserved and have to be merged manually.
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
_Note:_ The logarithm to a different base can be calculated with `z.log().div(Math.log(base))`.
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
boolean isFinite()
Checks if the given number is finite
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() |
Geometric Equivalence
===
Complex numbers can also be seen as a vector in the 2D space. Here is a simple overview of basic operations and how to implement them with complex.js:
New vector
```js
var v1 = new Complex(1, 0);
var v2 = new Complex(1, 1);
```
Scale vector
```js
scale(v1, factor):= v1.mul(factor)
```
Vector norm
```js
norm(v):= v.abs()
```
Translate vector
```js
translate(v1, v2):= v1.add(v2)
```
Rotate vector around center
```js
rotate(v, angle):= v.mul({abs: 1, arg: angle})
```
Rotate vector around a point
```js
rotate(v, p, angle):= v.sub(p).mul({abs: 1, arg: angle}).add(p)
```
Distance to another vector
```js
distance(v1, v2):= v1.sub(v2).abs()
```
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 `equals()` 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:
```bash
bower install complex.js
```
or
```bash
npm install complex.js
```
Using Complex.js with the browser
===
```html
<script src="complex.js"></script>
<script>
console.log(Complex("4+3i"));
</script>
```
Using Complex.js with require.js
===
```html
<script src="require.js"></script>
<script>
requirejs(['complex.js'],
function(Complex) {
console.log(Complex("4+3i"));
});
</script>
```
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
```bash
npm test
```
Copyright and licensing
===
Copyright (c) 2015, [Robert Eisele](http://www.xarg.org/)
Dual licensed under the MIT or GPL Version 2 licenses.