complex

Complex
=======

Complex is a additional Type to deal with Complex Numbers in JavaScript. It
provides several methods to add, multiply numbers as well as calculate the
magnitude and angle in the complex plane.

!Screenshot

Node
----

You can get this package with NPM:

npm install Complex

``js
var Complex = require('Complex');
console.log(new Complex(3, 4).abs()); // 5
`

Browser
-------

Complex can be built for the browser with wrapup
or other tools that can generate browser JS from Node packages.

Testing
-------

Testing is done with Mocha and Expect.js:

# install dependencies
npm install
# run the tests in node
./node_modules/.bin/mocha test/Complex.js

or testing in the browser:

# install dependencies
npm install
# run a small node server
node ./test/server.js
# run tests
google-chrome http://localhost:3000

API Documentation
-----------------

$3

`js
var z = new Complex(real im);
`

#### Arguments:

1. real (number) the real part of the number
2. im (number) the imaginary part of the number

$3

A in line function like Number.from.

`js
var z = Complex.from(real[, im]);
`

#### Arguments:

1. real (number) the real part of the number
2. im (number, optional) the imaginary part of the number

Or

1. real (string) a string representation of the number, for example 1+4i

#### Examples:

`js
var z = Complex.from(2, 4);
var z = Complex.from(5);
var z = Complex.from('2+5i');
`

$3

Creates a complex instance from a polar representation: re^(phii) = r (cos(phi) + i sin(phi))

`js
var z = Complex.fromPolar(r, phi);
`

#### Arguments:

1. r (number) the radius/magnitude of the number
2. phi (number) the angle/phase of the number

$3

A instance of the imaginary unit i

`js
var i = Complex.i;
`

$3

A instance for the real number 1

`js
var one = Complex.one;
`

$3

Sets the real and imaginary properties a and b from a + bi

`js
myComplex.fromRect(real, im);
`

#### Arguments:

1. real (number) the real part of the number
2. im (number) the imaginary part of the number

$3

Sets the a and b in a + bi from a polar representation.

`js
myComplex.fromPolar(r, phi);
`

#### Arguments:

1. r (number) the radius/magnitude of the number
2. phi (number) the angle/phase of the number

$3

Sets the precision of the numbers. Similar to Number.prototype.toPrecision. Useful befor printing the number with the toString method.

`js
myComplex.toPrecision(k);
`

#### Arguments:

1. k (number) An integer specifying the number of significant digits

$3

Formats a number using fixed-point notation. Similar to Number.prototype.toFixed. Useful before printing the number with the toString method.

`js
myComplex.toFixed(k);
`

#### Arguments:

1. k (number) The number of digits to appear after the decimal point; this may be a value between 0 and 20, inclusive, and implementations may optionally support a larger range of values. If this argument is omitted, it is treated as 0

$3

Finalizes the instance. The number will not change and any other method call will return a new instance.
Very useful when a complex instance should stay constant. For example the Complex.i variable is a finalized instance.

`js
myComplex.finalize();
`

$3

Calculates the magnitude of the complex number

`js
myComplex.magnitude();
`

#### Alias:

- abs

$3

Calculates the angle with respect to the real axis, in radians.

`js
myComplex.angle();
`

#### Aliases

- arg
- phase

$3

Calculates the conjugate of the complex number (multiplies the imaginary part with -1)

`js
myComplex.conjugate();
`

$3

Negates the number (multiplies both the real and imaginary part with -1)

`js
myComplex.negate();
`

$3

Multiplies the number with a real or complex number

`js
myComplex.multiply(z);
`

#### Arguments:

1. z (number, complex) the number to multiply with

#### Alias:

- mult

$3

Divides the number by a real or complex number

`js
myComplex.divide(z);
`

#### Arguments:

1. z (number, complex) the number to divide by

#### Alias:

- div

$3

Adds a real or complex number

`js
myComplex.add(z);
`

#### Arguments:

1. z (number, complex) the number to add

$3

Subtracts a real or complex number

`js
myComplex.subtract(z);
`

#### Arguments:

1. z (number, complex) the number to subtract

#### Alias:

- sub

$3

Returns the base to the exponent

`js
myComplex.pow(z);
`

#### Arguments:

1. z (number, complex) the exponent

$3

Returns the square root

`js
myComplex.sqrt();
`

$3

Returns the natural logarithm (base E)

`js
myComplex.log([k]);
`

#### Arguments:

1. k (number) the actual answer has a multiplicity (ln(z) = ln|z| + arg(z)) where arg(z) can return the same for different angles (every 2*pi), with this argument you can define which answer is required

$3

Calculates the e^z where the base is E and the exponential the complex number.

`js
myComplex.exp();
`

$3

Calculates the sine of the complex number

`js
myComplex.sin();
`

$3

Calculates the cosine of the complex number

`js
myComplex.cos();
`

$3

Calculates the tangent of the complex number

`js
myComplex.tan();
`

$3

Calculates the hyperbolic sine of the complex number

`js
myComplex.sinh();
`

$3

Calculates the hyperbolic cosine of the complex number

`js
myComplex.cosh();
`

$3

Calculates the hyperbolic tangent of the complex number

`js
myComplex.tanh();
`

$3

Returns a new Complex instance with the same real and imaginary properties

`js
myComplex.clone();
`

$3

Returns a string representation of the complex number

`js
myComplex.toString();
`


#### Examples:

`js
new Complex(1, 2).toString(); // 1+2i
new Complex(0, 1).toString(); // i
new Complex(4, 0).toString(); // 4
new Complex(1, 1).toString(); // 1+i
'my Complex Number is: ' + (new Complex(3, 5)); // 'my Complex Number is: 3+5i
`

$3

Checks if the real and imaginary components are equal to the passed in compelex components.

`js
myComplex.equals(z);
`

$3

1. z (number, complex) the complex number to compare with

$3

`js
new Complex(1, 4).equals(new Complex(1, 4)); // true
new Complex(1, 4).equals(new Complex(1, 3)); // false
``

MIT License

Copyright (c) 2014 Arian Stolwijk

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.