polar-0.0.0: Complex numbers in polar form

Data.Complex.Polar

Synopsis

Documentation

data RealFloat a => Polar 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 magnitude and its phase in radians.

Instances

 Typeable1 Polar RealFloat a => Eq (Polar a) RealFloat a => Floating (Polar a) RealFloat a => Fractional (Polar a) (Data a, RealFloat a) => Data (Polar a) RealFloat a => Num (Polar a) (Read a, RealFloat a) => Read (Polar a) RealFloat a => Show (Polar a)

fromPolar :: RealFloat a => Polar a -> Complex aSource

Convert to rectangular form.

fromComplex :: RealFloat a => Complex a -> Polar aSource

Convert to polar form.

realPart :: RealFloat a => Polar a -> aSource

Extracts the real part of a complex number.

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

Extracts the imaginary part of a complex number.

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

The conjugate of a complex number.

mkPolar :: RealFloat a => a -> a -> Polar aSource

Form a complex number from polar components of magnitude and phase. Phase is wrapped into (-pi,pi].

cis :: RealFloat a => a -> Polar aSource

`cis t` is a complex value with magnitude `1` and phase `t` (modulo `2*pi`).

polar :: RealFloat a => Polar 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 => Polar a -> aSource

The nonnegative magnitude of a complex number.

phase :: RealFloat a => Polar a -> aSource

The phase of a complex number, in the range `(-pi, pi]`. If the magnitude is zero, then so is the phase.