## README

# Immutable-Complex

This is a fork of the original Complex library of Arian Stolwijk. Thanks for the initial work!

It changes one fundamental thing and some details:

## Fundamental Change

The Complex Objects are now **immutable**, in the sense that when applying
mathematical operations on an instance of Complex doesn't change its value,
but it returns a **new** instance with the new value. I need this for my math.

Consequently, the finalize method was removed.

## Changes in Details

I changed the name of the imaginary part from "im" to "imag", because it is more verbose and because it reminds me of the API for complex numbers in Python.

I added an operator like API as aliases for existing functions. You can access them via the brackets

`c['='](d)`

New aliases are:`** => pow`

`* => multiply`

`/ => divide`

`+ => add`

`- => subtract`

`= => equals`

Used like this:

```
var c = new Complex(1,1);
c.add === c['+']; // true
// thus:
var cc = c['+'](c)
, cc2 = c.add(c)
;
cc['='](cc2); // true
```

## About:

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.

## Node

You can get this package with NPM:

```
npm install ComplexImmutable
```

```
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

### Complex constructor:

```
var z = new Complex(real, imag);
```

#### Arguments:

- real (number) the real part of the number
- imag (number) the imaginary part of the number

### Function: Complex.from

A in line function like Number.from.

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

#### Arguments:

- real (number) the real part of the number
- imag (number,
*optional*) the imaginary part of the number

Or

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

#### Examples:

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

### Function: Complex.fromPolar

Creates a complex instance from a polar representation: `r*e^(phi*i) = r (cos(phi) + i sin(phi))`

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

#### Arguments:

- r (number) the radius/magnitude of the number
- phi (number) the angle/phase of the number

### Constant: Complex.i

A instance of the imaginary unit `i`

```
var i = Complex.i;
```

### Constant: Complex.one

A instance for the real number `1`

```
var one = Complex.one;
```

### Method: fromRect

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

```
myComplex.fromRect(real, imag);
```

#### Arguments:

- real (number) the real part of the number
- imag (number) the imaginary part of the number

### Method: fromPolar

Sets the a and b in `a + bi`

from a polar representation.

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

#### Arguments:

- r (number) the radius/magnitude of the number
- phi (number) the angle/phase of the number

### Method: toPrecision

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

```
myComplex.toPrecision(k);
```

#### Arguments:

- k (number) An integer specifying the number of significant digits

### Method: toFixed

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

```
myComplex.toFixed(k);
```

#### Arguments:

- 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

### Method: magnitude

Calculates the magnitude of the complex number

```
myComplex.magnitude();
```

#### Alias:

- abs

### Method: angle

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

```
myComplex.angle();
```

#### Aliases

- arg
- phase

### Method: conjugate

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

```
myComplex.conjugate();
```

### Method: negate

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

```
myComplex.negate();
```

### Method: multiply

Multiplies the number with a real or complex number

```
myComplex.multiply(z);
```

#### Arguments:

- z (number, complex) the number to multiply with

#### Alias:

- mult

### Method: divide

Divides the number by a real or complex number

```
myComplex.divide(z);
```

#### Arguments:

- z (number, complex) the number to divide by

#### Alias:

- div
- /

### Method: add

Adds a real or complex number

```
myComplex.add(z);
```

#### Arguments:

- z (number, complex) the number to add

#### Alias:

### Method: subtract

Subtracts a real or complex number

```
myComplex.subtract(z);
```

#### Arguments:

- z (number, complex) the number to subtract

#### Alias:

- sub

### Method: pow

Returns the base to the exponent

```
myComplex.pow(z);
```

#### Arguments:

- z (number, complex) the exponent

#### Alias:

- **

### Method: sqrt

Returns the square root

```
myComplex.sqrt();
```

### Method: log

Returns the natural logarithm (base `E`

)

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

#### Arguments:

- 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

### Method: exp

Calculates the `e^z`

where the base is `E`

and the exponential the complex number.

```
myComplex.exp();
```

### Method: sin

Calculates the sine of the complex number

```
myComplex.sin();
```

### Method: cos

Calculates the cosine of the complex number

```
myComplex.cos();
```

### Method: tan

Calculates the tangent of the complex number

```
myComplex.tan();
```

### Method: sinh

Calculates the hyperbolic sine of the complex number

```
myComplex.sinh();
```

### Method: cosh

Calculates the hyperbolic cosine of the complex number

```
myComplex.cosh();
```

### Method: tanh

Calculates the hyperbolic tangent of the complex number

```
myComplex.tanh();
```

### Method: clone

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

```
myComplex.clone();
```

### Method: toString

Returns a string representation of the complex number

```
myComplex.toString();
```

#### Examples:

```
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
```

### Method: Equals

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

```
myComplex.equals(z);
```

### Arguments:

- z (number, complex) the complex number to compare with

#### Alias:

- =

### Examples:

```
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, Lasse Fister

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.