base-4.2.0.1: Basic librariesSource codeContentsIndex
Data.Complex
Portabilityportable
Stabilityprovisional
Maintainerlibraries@haskell.org
Contents
Rectangular form
Polar form
Conjugate
Description
Complex numbers.
Synopsis
data RealFloat a => Complex a = !a :+ !a
realPart :: RealFloat a => Complex a -> a
imagPart :: RealFloat a => Complex a -> a
mkPolar :: RealFloat a => a -> a -> Complex a
cis :: RealFloat a => a -> Complex a
polar :: RealFloat a => Complex a -> (a, a)
magnitude :: RealFloat a => Complex a -> a
phase :: RealFloat a => Complex a -> a
conjugate :: RealFloat a => Complex a -> Complex a
Rectangular form
data RealFloat a => Complex a Source

Complex numbers are an algebraic type.

For a complex number z, abs z is a number with the magnitude of z, but oriented in the positive real direction, whereas signum z has the phase of z, but unit magnitude.

Constructors
!a :+ !aforms a complex number from its real and imaginary rectangular components.
show/hide Instances
realPart :: RealFloat a => Complex a -> aSource
Extracts the real part of a complex number.
imagPart :: RealFloat a => Complex a -> aSource
Extracts the imaginary part of a complex number.
Polar form
mkPolar :: RealFloat a => a -> a -> Complex aSource
Form a complex number from polar components of magnitude and phase.
cis :: RealFloat a => a -> Complex aSource
cis t is a complex value with magnitude 1 and phase t (modulo 2*pi).
polar :: RealFloat a => Complex a -> (a, a)Source
The function polar takes a complex number and returns a (magnitude, phase) pair in canonical form: the magnitude is nonnegative, and the phase in the range (-pi, pi]; if the magnitude is zero, then so is the phase.
magnitude :: RealFloat a => Complex a -> aSource
The nonnegative magnitude of a complex number.
phase :: RealFloat a => Complex a -> aSource
The phase of a complex number, in the range (-pi, pi]. If the magnitude is zero, then so is the phase.
Conjugate
conjugate :: RealFloat a => Complex a -> Complex aSource
The conjugate of a complex number.
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