base-4.7.0.2: Basic libraries

Copyright (c) The University of Glasgow 2001 BSD-style (see the file libraries/base/LICENSE) libraries@haskell.org provisional portable Trustworthy Haskell2010

Data.Complex

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 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 Source

Extracts the real part of a complex number.

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

Extracts the imaginary part of a complex number.

# Polar form

mkPolar :: RealFloat a => a -> a -> Complex a Source

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

cis :: RealFloat a => a -> Complex a Source

`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 -> a Source

The nonnegative magnitude of a complex number.

phase :: RealFloat a => Complex a -> a Source

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 Source

The conjugate of a complex number.