Complex

Synopsis

Documentation

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 -> aSource

Extracts the real part of a complex number.

imagPart :: RealFloat a => Complex a -> aSource

Extracts the imaginary part of a complex number.

conjugate :: RealFloat a => Complex a -> Complex aSource

The conjugate of a complex number.

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.