Complex
module Complex
Complex numbers with real and imaginary components, plus polar conversion.
Components accept Number values. Trigonometric angles are in radians.
using Complex
let z = Rectangular { re: 3, im: 4 }
z.abs # => 5.0ZERO constant
The additive identity, +0 + 0i+.
ONE constant
The multiplicative identity, +1 + 0i+.
I constant
The imaginary unit, +0 + 1i+.
NEG_I constant
The negative imaginary unit, 0 - 1i.
fromPolar
fromPolar(radius: Number, theta: Number) -> RectangularConstructs a complex number from a radius and an angle in radians.
Parameters
radius- distance from the origin
theta- angle in radians
Returns the rectangular representation
Examples
A quarter turn
Complex.fromPolar(2, Math.PI / 2).im # approximately 2.0fromPolarCoordinates
fromPolarCoordinates(polar: Polar) -> RectangularConstructs a complex number from a Polar value.
Parameters
polar- radius and angle in radians
Returns the rectangular representation
Examples
Complex.fromPolarCoordinates(Polar { radius: 3, theta: 0 }).re # => 3.0conjugateOf
conjugateOf(value: Rectangular) -> RectangularReturns the conjugate of a complex number.
Parameters
value- the number to conjugate
Returns the number with its imaginary sign reversed
Examples
Complex.conjugateOf(Complex.I).im # => -1record Rectangular
A complex number in rectangular form: re is the real part and im is the imaginary part.
Fields
Implements Showable.
Functions
showValue Showable
showValue : StringRenders the number in rectangular form, such as +3+4i+.
Returns the real and signed imaginary components
Examples
(Rectangular { re: 3, im: -4 }).showValue # => "3-4i"+
+(other: Rectangular) -> RectangularAdds two complex numbers component by component.
Examples
(Rectangular { re: 1, im: 2 } + Complex.I).im # => 3-
-(other: Rectangular) -> RectangularSubtracts other from this complex number.
Examples
(Rectangular { re: 1, im: 2 } - Complex.I).im # => 1*
*(other: Rectangular) -> RectangularMultiplies two complex numbers.
Examples
(Complex.I * Complex.I).re # => -1/
/(other: Rectangular) -> RectangularDivides by other using the complex conjugate formula. The divisor must be non-zero.
Examples
(Complex.I / Complex.I).re # => 1.0conjugate
conjugate : RectangularReturns the complex conjugate, negating the imaginary part.
Examples
let conjugated: Rectangular = Complex.conjugateOf(Complex.I)
conjugated.im # => -1sqrt
sqrt : RectangularReturns the principal square root. The result's argument lies in the right half-plane.
Examples
(Rectangular { re: -1, im: 0 }).sqrt.im # approximately 1.0exp
exp : RectangularReturns e raised to this complex number.
Examples
Complex.ZERO.exp.re # => 1.0log
log : RectangularReturns the principal natural logarithm. Zero has no logarithm.
Examples
Complex.ONE.log.re # => 0.0^
^(exponent: Number) -> RectangularRaises this number to a real power using the principal argument.
Examples
(Complex.I ^ 2).re # approximately -1.0absSquared
absSquared : NumberReturns the square of the magnitude.
Returns real² + imaginary²
Examples
(Rectangular { re: 3, im: 4 }).absSquared # => 25abs
abs : FloatReturns the magnitude of this complex number.
Returns distance from the origin
Examples
(Rectangular { re: 3, im: 4 }).abs # => 5.0From Showable
record Polar
A complex number in polar form, with a non-negative radius and angle in radians.
Fields
Implements Showable.
Functions
showValue Showable
showValue : StringRenders the radius and angle in radians.
Returns the polar coordinates
Examples
(Polar { radius: 2, theta: 0 }).showValue # => "(2, 0)"rectangular
rectangular : RectangularConverts these polar coordinates to a complex number.
Returns the rectangular representation
Examples
(Polar { radius: 2, theta: 0 }).rectangular.re # => 2.0