Complex

The Complex module provides complex number operations (numbers with real and imaginary parts).

Creation

Complex.new

Float -> Float -> Complex

Creates a complex number from real and imaginary parts.

c = Complex.new 3.0 4.0
println (Complex.to-string c)
# => "3+4i"

Complex.from-real

Float -> Complex

Creates a complex from a real number (imaginary = 0).

Complex.from-imaginary

Float -> Complex

Creates a complex from an imaginary number (real = 0).

Complex.from-polar

Float -> Float -> Complex

Creates from polar coordinates (magnitude, phase in radians).

Complex.parse

String -> Option Complex

Parses a string like "3+4i" or "5i".

Complex.i

() -> Complex

Returns the imaginary unit (0+1i).

Accessors

Complex.real

Complex -> Float

Returns the real part.

Complex.imag

Complex -> Float

Returns the imaginary part.

Arithmetic

Complex.add

Complex -> Complex -> Complex

Adds two complex numbers.

Complex.subtract

Complex -> Complex -> Complex

Subtracts two complex numbers.

Complex.multiply

Complex -> Complex -> Complex

Multiplies two complex numbers.

Complex.divide

Complex -> Complex -> Option Complex

Divides two complex numbers. Returns None for division by zero.

Complex.negate

Complex -> Complex

Negates (changes sign of both parts).

Complex.conjugate

Complex -> Complex

Returns the complex conjugate (negates imaginary part).

Complex.reciprocal

Complex -> Option Complex

Returns 1/z. Returns None for zero.

Complex.scale

Complex -> Float -> Complex

Multiplies by a real scalar.

Properties

Complex.magnitude

Complex -> Float

Returns the magnitude (absolute value).

c = Complex.new 3.0 4.0
println (Complex.magnitude c)
# => 5.0

Complex.magnitude-squared

Complex -> Float

Returns magnitude squared (avoids sqrt).

Complex.phase

Complex -> Float

Returns the phase angle in radians.

Predicates

Complex.zero?

Complex -> Bool

Returns true if zero.

Complex.real?

Complex -> Bool

Returns true if purely real (imag = 0).

Complex.imaginary?

Complex -> Bool

Returns true if purely imaginary (real = 0).

Complex.eq?

Complex -> Complex -> Bool

Tests equality.

Math Functions

Complex.exp

Complex -> Complex

Complex exponential (e^z).

Complex.log

Complex -> Option Complex

Complex natural logarithm.

Complex.sqrt

Complex -> Complex

Complex square root.

Complex.pow

Complex -> Complex -> Option Complex

Raises to a complex power.

Complex.pow-int

Complex -> Int -> Complex

Raises to an integer power.

Complex.sin

Complex -> Complex

Complex sine.

Complex.cos

Complex -> Complex

Complex cosine.

Complex.tan

Complex -> Option Complex

Complex tangent.

Conversion

Complex.to-polar

Complex -> {magnitude, phase}

Converts to polar form.

Complex.to-string

Complex -> String

Converts to string like "3+4i".