Copyright | (c) The University of Glasgow 2001 |
---|---|

License | BSD-style (see the file libraries/base/LICENSE) |

Maintainer | libraries@haskell.org |

Stability | provisional |

Portability | portable |

Safe Haskell | Trustworthy |

Language | Haskell2010 |

Complex numbers.

## Synopsis

- data Complex a = !a :+ !a
- realPart :: Complex a -> a
- imagPart :: Complex a -> a
- mkPolar :: Floating a => a -> a -> Complex a
- cis :: Floating a => a -> Complex a
- polar :: RealFloat a => Complex a -> (a, a)
- magnitude :: RealFloat a => Complex a -> a
- phase :: RealFloat a => Complex a -> a
- conjugate :: Num a => Complex a -> Complex a

# Rectangular form

Complex numbers are an algebraic type.

For a complex number `z`

,

is a number with the magnitude of `abs`

z`z`

,
but oriented in the positive real direction, whereas

has the phase of `signum`

z`z`

, but unit magnitude.

The `Foldable`

and `Traversable`

instances traverse the real part first.

Note that `Complex`

's instances inherit the deficiencies from the type
parameter's. For example, `Complex Float`

's `Ord`

instance has similar
problems to `Float`

's.

!a :+ !a infix 6 | forms a complex number from its real and imaginary rectangular components. |

#### Instances

# Polar form

mkPolar :: Floating a => a -> a -> Complex a Source #

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