module Progwerkstatt where

-- 1.1

data Complex1 = Comp1 Float Float
   deriving(Show)

mkComplex1 :: Float -> Float -> Complex1
mkComplex1 r i = Comp1 r i


data Complex2 a = Comp2 a a
   deriving(Show)

mkComplex2 :: a -> a -> Complex2 a
mkComplex2 r i = Comp2 r i


-- 1.2

getReal1 :: Complex1 -> Float
getReal1 ( Comp1 r _ ) = r

getImag1 :: Complex1 -> Float
getImag1 ( Comp1 _ i ) = i

getReal2 :: Complex2 a -> a
getReal2 ( Comp2 r _ ) = r

getImag2 :: Complex2 a -> a
getImag2 ( Comp2 _ i ) = i


-- 1.3

addComplex1 :: Complex1 -> Complex1 -> Complex1
addComplex1 ( Comp1 r1 i1 ) ( Comp1 r2 i2 ) = Comp1 (r1 + r2) (i1 + i2) 

addComplex2 :: Num a => Complex2 a -> Complex2 a -> Complex2 a
addComplex2 ( Comp2 r1 i1 ) ( Comp2 r2 i2 ) = Comp2 (r1 + r2) (i1 + i2)

-- 2

instance Eq Complex1 where
   (Comp1 r1 i1) == (Comp1 r2 i2) = (r1 == r2 ) && (i1 == i2)

instance Num Complex1 where
   (Comp1 r1 i1) + (Comp1 r2 i2) = Comp1 (r1 + r2) (i1 + i2)
   (Comp1 r1 i1) - (Comp1 r2 i2) = Comp1 (r1 - r2) (i1 - i2)
   (Comp1 r1 i1) * (Comp1 r2 i2) = Comp1 (r1 * r2) (i1 * i2)
   abs (Comp1 r1 i1) = Comp1 (r1 * r1 + i1 * i1) 0