Data.Complex

Complex numbers.

Rectangular form

data Complex a

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 infix 6

forms a complex number from its real and imaginary rectangular components.

Instances

Eq a ⇒ Eq (Complex a)

RealFloat a ⇒ Floating (Complex a)

RealFloat a ⇒ Fractional (Complex a)

Data a ⇒ Data (Complex a)

RealFloat a ⇒ Num (Complex a)

Read a ⇒ Read (Complex a)

Show a ⇒ Show (Complex a)

Typeable (★ → ★) Complex

realPart ∷ RealFloat a ⇒ Complex a → a

Extracts the real part of a complex number.

imagPart ∷ RealFloat a ⇒ Complex a → a

Extracts the imaginary part of a complex number.

Polar form

mkPolar ∷ RealFloat a ⇒ a → a → Complex a

Form a complex number from polar components of magnitude and phase.

cis ∷ RealFloat a ⇒ a → Complex a

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

polar ∷ RealFloat a ⇒ Complex a → (a, a)

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

The nonnegative magnitude of a complex number.

phase ∷ RealFloat a ⇒ Complex a → a

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

The conjugate of a complex number.