js-math-complex


math-complex.js
===============

Complex Number for JavaScript

USAGE
-----

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```html

``

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``javascript
require('./math-complex.js');
``

SYNOPSIS
--------

``javascript
var cplx = Math.Complex, // for convenience
j = cplx(0, 1);
j.mul(Math.PI).exp() + ''; // -1+1.2246063538223773e-16i
// ditto
Math.Complex.exp(cplx(0, Math.PI));
``

DESCRIPTION
-----------

This module implements complex number arithmetics. Basic arithmetics + All arithmetic functions in Math are supported.

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#### Math.Complex( re [, im] )

Constructor. im === 0 if omitted.

``javascript
var z = Math.Complex(1,2);
z.re === 1;
z.im === 2;
``

#### Math.Complex.polar( abs, arg )

Constructor in polar form.

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In the followin example z is a complex number object. Unless otherwise stated, all methods below return complex number objects.

#### z.eq( z1 )

returns true if z equals z1, false otherwise.

#### z.ne( z1 )

The opposite of z.eq( z1 )

#### z.abs()

returns the absolute value in Number.

#### z.arg()

returns the argument in Number.

#### z.neg()

returns - z

#### z.con()

returns the conjugate.

``javascript
Math.Complex(re, im).con().eq(Math.Complex(re, -im));
``

#### z.norm()

returns the norm in Number.

#### z.add( z1 )

z + z1. z1 can be either complex number or real number If z1 is a real number (Number object, that is), it is automatically converted to complex number before the calculation. This applies to all binary methods.

#### z.sub( z1 )

z - z1

#### z.mul( z1 )

z z1*

#### z.div( z1 )

z / z1

#### z.exp()

Copmplex version of Math.exp( z ) .

#### z.log()

Copmplex version of Math.log( z ) .

#### z.pow( z1 )

Copmplex version of Math.exp( z, z1 ) .

#### z.sin()

Copmplex version of Math.sin( z ) .

#### z.cos()

Copmplex version of Math.cos( z ) .

#### z.tan()

Copmplex version of Math.tan( z ) .

#### z.asin()

Copmplex version of Math.asin( z ) .

#### z.acos()

Copmplex version of Math.acos( z ) .

#### z.atan()

Copmplex version of Math.atan( z ) .

#### z.approx(z1)

z is approximately equal to z1.

``
delta abs(z - z1)
------- < EPSILON <=> ----------- < 2*EPSILON
average abs(z + z1)
``

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All methods above can also be accessed in functional form which is handy with with.

``javascript
// does not work in strict mode
with(Math.Complex){
console.log(atan2(1,1)) // { re: 0.7853981633974483, im: 0 }
}
```