Class

Complex

Represents a numerical complex value backed by

`decimal.js`

components.

remarks

This class is a numerical helper used by algorithms such as polynomial root solving. It is distinct from Nerdamer's symbolic complex expressions: it does not parse expressions, carry symbolic structure, or implement branch-sensitive transcendental functions. Component arithmetic follows the active global

`decimal.js`

precision. Arithmetic methods return new

`Complex`

objects rather than modifying the receiver. The Complex.re and Complex.im fields are public, however, so callers can reassign components directly.

Members

abs(): DecimalMethod

Computes the modulus

`sqrt(re^2 + im^2)`

Returns

Decimal — A new Decimal containing the nonnegative magnitude.

add(other: Complex): ComplexMethod

Adds another complex value component-wise.

Parameters

Name	Type	Description
`other`	`Complex`	Complex value to add.

Returns

Complex — A new complex sum.

conjugate(): ComplexMethod

Returns the complex conjugate

`re - im*i`

Returns

Complex — A new complex value with the imaginary component negated.

Complex(re: number | Decimal, im: number | Decimal): ComplexConstructor

Creates a numerical complex value.

remarks

Existing Decimal components are retained by reference; numeric inputs are converted to new Decimal values.

`decimal.js`

arithmetic itself returns new Decimal objects.

Parameters

Name	Type	Description
`re`	`number \| Decimal`	Real component.
`im`	`number \| Decimal`	Imaginary component; defaults to zero.

Returns

Complex

create(re: number | Decimal, im: number | Decimal): ComplexMethod

Creates a numerical complex value from Decimal or native-number components.

Parameters

Name	Type	Description
`re`	`number \| Decimal`	Real component.
`im`	`number \| Decimal`	Imaginary component; defaults to zero.

Returns

Complex — A new `Complex` value.

div(other: Complex): ComplexMethod

Divides this complex value by another using the standard rectangular formula.

remarks

Division rejects an exactly zero squared modulus. No numerical tolerance is applied at this arithmetic layer; iterative algorithms are responsible for choosing any tolerance appropriate to their convergence logic.

throws

DivisionByZeroError Thrown when both components of

`other`

are exactly zero at the current Decimal value.

Parameters

Name	Type	Description
`other`	`Complex`	Complex divisor.

Returns

Complex — A new complex quotient.

im: DecimalProperty

Imaginary component.

mul(other: Complex): ComplexMethod

Multiplies two rectangular complex values.

Parameters

Name	Type	Description
`other`	`Complex`	Complex factor.

Returns

Complex — A new complex product.

neg(): ComplexMethod

Returns the additive inverse of this complex value.

Returns

Complex — A new complex value with both components negated.

re: DecimalProperty

Real component.

scale(s: number | Decimal): ComplexMethod

Multiplies both complex components by a real scalar.

Parameters

Name	Type	Description
`s`	`number \| Decimal`	Decimal or native-number scale factor.

Returns

Complex — A new scaled complex value.

sub(other: Complex): ComplexMethod

Subtracts another complex value component-wise.

Parameters

Name	Type	Description
`other`	`Complex`	Complex value to subtract.

Returns

Complex — A new complex difference.