Just a dopey implementation of a Complex type in PureScript

Complex.purs

module Data.Complex where

data Complex = Complex Number Number

instance showComplex :: Show Complex where
  show (Complex x y) = show x ++ " + " ++ show y ++ "i"

instance eqComplex :: Eq Complex where
  (==) (Complex x y) (Complex x' y') = (x == x') && (y == y')
  (/=) (Complex x y) (Complex x' y') = (x /= x') || (y /= y')

complexAdd :: Complex -> Complex -> Complex
complexAdd (Complex x y) (Complex x' y') = Complex (x + x') (y + y')
complexMultiply :: Complex -> Complex -> Complex
complexMultiply (Complex x y) (Complex x' y') = Complex (x * x' - y * y') (x * y' + x' * y)

instance semiringComplex :: Semiring Complex where
  (+) = complexAdd
  (*) = complexMultiply
  zero = Complex 0 0
  one = Complex 1 0

complexSubtract :: Complex -> Complex -> Complex
complexSubtract (Complex x y) (Complex x' y') = Complex (x - x') (y - y')

instance ringComplex :: Ring Complex where
  (-) = complexSubtract

complexDivide :: Complex -> Complex -> Complex
complexDivide (Complex x y) (Complex x' y') = Complex x'' y'' where
  x'' = (x * x' - y * y') / (x' * x' + y' * y')
  y'' = (x' * y - x * y') / (x' * x' + y' * y')