Complex - Documentation

new Complex(arg1, arg2)

Source:

index.js, line 1

Creates a new Complex Number.

Parameters:

Name	Type	Description
`arg1`	number	The real part of the Complex Number
`arg2`	number	The imaginary part of the Complex Number

Members

(static) NaN

Source:

index.js, line 80

It represents NaN in this library. It is equivalent to new Complex(NaN).

It is important to know that this library does not introduce the concept of Complex Infinity, all Infinity in this library are represented by Complex.NaN.

(static) ONE

Source:

index.js, line 83

(static) ZERO

Source:

index.js, line 86

(static) PI

Source:

index.js, line 89

(static) E

Source:

index.js, line 92

(static) EPSILON

Source:

index.js, line 100

It represents the value of 5e-16, which is the smallest number considered as non-zero in this library. In the other words, any number less than Complex.EPSILON is considered as 0.

Note that Complex.EPSILON is number instead of instance of Complex.

Methods

getArgument() → {number}

Source:

core/instance/getArgument.js, line 12

Calculates the argument of a Complex Number which is restricted to the interval [ 0, 2π ).

The argument of the Complex Number is the angle between positive real-axis and the vector representing the Complex Number on Complex plane.

If the given Complex Number is considered as 0, returns undefined.

Returns:

The argument of the Complex Number

Type: number

getImaginary() → {number}

Source:

core/instance/getImaginary.js, line 7

Gets the imaginary part of a Complex Number.

Returns:

The imaginary part of the Complex Number

Type: number

getModulus() → {number}

Source:

core/instance/getModulus.js, line 10

Calculates the modulus of a Complex Number.

The modulus of the complex number is the length of the vector representing the complex number on complex plane.

Returns:

The modulus of the Complex Number

Type: number

getReal() → {number}

Source:

core/instance/getReal.js, line 7

Gets the real part of a Complex Number.

Returns:

The real part of the Complex Number

Type: number

toString() → {string}

Source:

core/instance/toString.js, line 7

Gets the stringified and formatted Complex Number.

Returns:

The stringified and formatted Complex Number

Type: string

(static) acos(num) → {Complex}

Source:

core/static/acos.js, line 8

Calculates the inverse cosine of a Complex Number.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number

Returns:

The result of inverse cosine function

Type: Complex

(static) acot(num) → {Complex}

Source:

core/static/acot.js, line 12

Calculates the inverse cotangent of a Complex Number. The domain of this function is C / { i , -i , 0 }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number except i, -i and 0

Returns:

The result of inverse cotangent function

Type: Complex

(static) acsc(num) → {Complex}

Source:

core/static/acsc.js, line 12

Calculates the inverse cosecant of a Complex Number. The domain of this function is C / { 0 }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number except 0

Returns:

The result of inverse cosecant function

Type: Complex

(static) add(num1, num2) → {Complex}

Source:

core/static/add.js, line 9

Calculates the sum of two Complex Number.

Parameters:

Name	Type	Description
`num1`	Complex	The Complex Number on the left of '+' operator.
`num2`	Complex	The Complex Number on the right of '+' operator.

Returns:

The sum of two Complex Numbers

Type: Complex

(static) asec(num) → {Complex}

Source:

core/static/asec.js, line 11

Calculates the inverse secant of a Complex Number. The domain of this function is C / { 0 }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number except 0

Returns:

The result of inverse secant function

Type: Complex

(static) asin(num) → {Complex}

Source:

core/static/asin.js, line 8

Calculates the inverse sine of a Complex Number.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number

Returns:

The result of inverse sine function

Type: Complex

(static) atan(num) → {Complex}

Source:

core/static/atan.js, line 11

Calculates the inverse tangent of a Complex Number. The domain of this function is C / { i , -i }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number except i and -i

Returns:

The result of inverse tangent function

Type: Complex

(static) conjugate(num) → {Complex}

Source:

core/static/conjugate.js, line 9

Calculates the complex conjugate of the Complex Number.

Parameters:

Name	Type	Description
`num`	Complex	Complex number

Returns:

The complex conjugate of the Complex Number

Type: Complex

(static) cos(num) → {Complex}

Source:

core/static/cos.js, line 8

Calculates the cosine of a Complex Number.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number

Returns:

The result of cosine function

Type: Complex

(static) cot(num) → {Complex}

Source:

core/static/cot.js, line 11

Calculates the cotangent of a Complex Number. The domain of this function is C / { kπ/2 : k is any integer }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number which is not the multiple of π/2

Returns:

The result of cotangent function

Type: Complex

(static) csc(num) → {Complex}

Source:

core/static/csc.js, line 11

Calculates the cosecant of a Complex Number. The domain of this function is C / { kπ : k is any integer }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number which is not the multiple of π

Returns:

The result of cosecant function

Type: Complex

(static) divide(num1, num2) → {Complex}

Source:

core/static/divide.js, line 12

Calculates the quotient of two Complex Number.

Note that if the denominator is considered as 0, returns Complex.NaN instead of Infinity.

Parameters:

Name	Type	Description
`num1`	Complex	The Complex Number on the left of '/' operator.
`num2`	Complex	The Complex Number on the right of '/' operator.

Returns:

The quotient of two Complex Numbers

Type: Complex

(static) exp(num) → {Complex}

Source:

core/static/exp.js, line 8

Calculates the exponential function with base E.

Parameters:

Name	Type	Description
`num`	Complex	Exponent

Returns:

The value of E to the power of num

Type: Complex

(static) inverse(num) → {number}

Source:

core/static/inverse.js, line 8

Calculates the inverse of the Complex Number.

Parameters:

Name	Type	Description
`num`	Complex	Complex Number

Returns:

Inverse of the Complex Number

Type: number

(static) isEqual(num1, num2, digitopt) → {boolean}

Source:

core/static/isEqual.js, line 18

Determines whether two Complex Numbers are considered as identical.

Two Complex Numbers are considered as identical if either both are NaN or both real and imaginary parts are extremely closed.

The test criterion is Math.abs(x - y) < 1 / (10 ** digit * 2). For default value 15, it should be 5e-16. That means if the difference of two numbers is less than 5e-16, they are considered as same value.

Parameters:

Name	Type	Attributes	Default	Description
`num1`	Complex			Complex Number
`num2`	Complex			Complex Number
`digit`	number	<optional>	`15`	Number of significant digits

Returns:

Returns true if two Complex Numbers are considered as identical

Type: boolean

(static) isNaN(num) → {boolean}

Source:

core/static/isNaN.js, line 8

Determines whether the Complex Number is NaN or not.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex number

Returns:

Returns true if one of real and imaginary part are NaN

Type: boolean

(static) log(num) → {number}

Source:

core/static/log.js, line 12

Calculates the natural log of the Complex Number.

Note that complex log is a multivalued function, and this function only provides the principal value by restricting the imaginary part to the interval [0, 2π).

Parameters:

Name	Type	Description
`num`	Complex	Complex Number

Returns:

Natural log of the Complex Number

Type: number

(static) multiply(num1, num2) → {Complex}

Source:

core/static/multiply.js, line 9

Calculates the product of two Complex Number.

Parameters:

Name	Type	Description
`num1`	Complex	The Complex Number on the left of '*' operator.
`num2`	Complex	The Complex Number on the right of '*' operator.

Returns:

The product of two Complex Numbers

Type: Complex

(static) pow(num, n) → {Complex}

Source:

core/static/pow.js, line 13

Calculates the power of the Complex Number. The exponent can be any real number or Complex Number

You can find the k-th root of complex number by setting the exponent to 1 / k. But you should know that it only returns one out of k possible solutions.

Parameters:

Name	Type	Description
`num`	Complex	Base
`n`	Complex \| number	Exponent

Returns:

The result of the exponentiation

Type: Complex

(static) sec(num) → {Complex}

Source:

core/static/sec.js, line 11

Calculates the secant of a Complex Number. The domain of this function is C / { (k + 0.5)π : k is any integer }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number which is not in the form of (k + 0.5)π

Returns:

The result of secant function

Type: Complex

(static) sin(num) → {Complex}

Source:

core/static/sin.js, line 8

Calculates the sine of a Complex Number.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number

Returns:

The result of sine function

Type: Complex

(static) subtract(num1, num2) → {Complex}

Source:

core/static/subtract.js, line 9

Calculates the difference of two Complex Number.

Parameters:

Name	Type	Description
`num1`	Complex	The Complex Number on the left of '-' operator.
`num2`	Complex	The Complex Number on the right of '-' operator.

Returns:

The difference of two Complex Numbers

Type: Complex

(static) tan(num) → {Complex}

Source:

core/static/tan.js, line 11

Calculates the tangent of a Complex Number. The domain of this function is C / { (k + 0.5)π : k is any integer }.

If the argument is out of its domain, it returns Complex.NaN.

Parameters:

Name	Type	Description
`num`	Complex	Any Complex Number which is not in the form of (k + 0.5)π

Returns:

The result of tangent function

Type: Complex