## Complex *0.1*

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.

### Details

- Author
- Arian Stolwijk
- Current version
- 0.1
- GitHub
- arian/Complex
- Downloads
- 1839
- Category
- Native
- Tags
- Report
- GitHub Issues

### How to use

Just include the file Complex.js into your page or require it in your ssjs script.

### Build

Build via Packager, requires MooTools Core to be registered to Packager already *(ty cpojer)*

./packager register /path/to/Complex ./packager build Complex/* > Complex

### Api Documentation

### Complex constructor:

var z = new Complex(real[, im]);

#### Arguments:

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

Or

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

#### Examples:

var z = new Complex(2, 4); var z = new Complex('2+5i');

### Function: Complex.from

A in line function like Number.from.

var z = Complex.from(real, im);

#### Arguments:

The same as the Complex constructor.

### 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, im);

#### Arguments:

- real (number) the real part of the number
- im (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: finalize

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.

myComplex.finalize();

### Method: magnitude

Calculates the magnitude of the complex number

myComplex.maginude();

#### Alias:

- abs

### Method: angle

Calculates the angle with the real axis.

myComplex.angle();

#### Aliases

- arg
- phase

### Method: conjungate

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

myComplex.conjungate();

### 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: devide

Devides the number by a real or complex number

myComplex.devide(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

### 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

### 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

### Examples:

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

### Additions To The Number Object

Each method of the Complex object is added to the Number object, so it is easy to use them together.

#### Example:

(3).add(new Complex(2, 4)).toString(); // 5+4i

### Method: toComplex

Returns a Complex instance where the real component is the value of the number.

myNumber.toComplex();

#### Example:

(3).toComplex().add(new Complex(3, 4)).toString(); // 6+4i

### Function: Number.from

Number.from accepts Complex instances. It will return the real component.

#### Example:

Number.from(new Complex(3, 4)); // 3

### Additions To The Math Object

The following functions are added to the Math object:

- Math.sinh - calculates the hyperbolic sine of a (real) number
- Math.cosh - calculates the hyperbolic cosine of a (real) number
- Math.tanh - calculates the hyperbolic tangent of a (real) number

### Additions To The Strnig Object

String implements the following methods:

### Method: toComplex

Parses a string like 3+5i into a Complex instance.

myString.toComplex();

#### Example:

'4+2i'.toComplex(); // a complex instance with the real component = 4 and the imaginary component = 2

### Discuss

**A note on comments here**: These comments are moderated. No comments will show up until they are approved. Comments that are not productive (i.e. inflammatory, rude, etc) will not be approved.

Found a bug in this plugin? Please report it this repository's Github Issues.

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