Data.Complex
 Portability portable Stability provisional Maintainer libraries@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 :+ !a forms a complex number from its real and imaginary rectangular components. Instances
 Typeable1 Complex RealFloat a => Eq (Complex a) RealFloat a => Floating (Complex a) RealFloat a => Fractional (Complex a) (Data a, RealFloat a) => Data (Complex a) RealFloat a => Num (Complex a) (Read a, RealFloat a) => Read (Complex a) RealFloat a => Show (Complex a)
 realPart :: RealFloat a => Complex a -> a Source
Extracts the real part of a complex number.
 imagPart :: RealFloat a => Complex a -> a Source
Extracts the imaginary part of a complex number.
Polar form
 mkPolar :: RealFloat a => a -> a -> Complex a Source
Form a complex number from polar components of magnitude and phase.
 cis :: RealFloat a => a -> Complex a Source
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 -> a Source
The nonnegative magnitude of a complex number.
 phase :: RealFloat a => Complex a -> a Source
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 Source
The conjugate of a complex number.