haskell98-1.1.0.1: Compatibility with Haskell 98

Complex

Synopsis

- data RealFloat a => Complex a = !a :+ !a
- realPart :: RealFloat a => Complex a -> a
- imagPart :: RealFloat a => Complex a -> a
- conjugate :: RealFloat a => Complex a -> Complex 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

# 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.