module Complex(Num(..)) where

import DComplex
import Magnitude
import Eq_Complex
import Show_Complex

instance  (RealFloat a) => Num (Complex a)  where
    (x:+y) + (x':+y')   =  (x+x') :+ (y+y')
    (x:+y) - (x':+y')   =  (x-x') :+ (y-y')
    (x:+y) * (x':+y')   =  (x*x'-y*y') :+ (x*y'+y*x')
    negate (x:+y)       =  negate x :+ negate y
    abs z               =  magnitude z :+ 0
    signum 0            =  0
    signum z@(x:+y)     =  x/r :+ y/r  where r = magnitude z
    fromInteger n       =  fromInteger n :+ 0