Data.Complex
 Portability portable Stability provisional Maintainer libraries@haskell.org
 Contents Rectangular form Polar form Conjugate
Description
Complex numbers.
Synopsis
 data 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 Complex a

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 !a forms a complex number from its real and imaginary rectangular components.
Instances
 Typeable1 Complex (RealFloat a, Eq a) => Eq (Complex a) RealFloat a => Floating (Complex a) RealFloat a => Fractional (Complex a) (RealFloat a, NFData a) => NFData (Complex a) RealFloat a => Num (Complex a) (RealFloat a, Read a) => Read (Complex a) (RealFloat a, Show a) => Show (Complex a)
realPart :: RealFloat a => Complex a -> a
Extracts the real part of a complex number.
imagPart :: RealFloat a => Complex a -> a
Extracts the imaginary part of a complex number.
Polar form
mkPolar :: RealFloat a => a -> a -> Complex a
Form a complex number from polar components of magnitude and phase.
cis :: RealFloat a => a -> Complex a
cis t is a complex value with magnitude 1 and phase t (modulo 2*pi).
polar :: RealFloat a => Complex a -> (a, a)
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 -> a
The nonnegative magnitude of a complex number.
phase :: RealFloat a => Complex a -> a
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 a
The conjugate of a complex number.
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