Portability	portable
Stability	provisional
Maintainer	libraries@haskell.org
Safe Haskell	Trustworthy

Data.Complex

Contents

Rectangular form
Polar form
Conjugate

Description

Complex numbers.

Synopsis

Rectangular form

data 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
Eq a => Eq (Complex a)
(Fractional (Complex a), RealFloat a) => Floating (Complex a)
(Num (Complex a), RealFloat a) => Fractional (Complex a)
(Typeable (Complex a), Data a) => Data (Complex a)
RealFloat a => Num (Complex a)
Read a => Read (Complex a)
Show a => Show (Complex a)

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.