Implemented the complex-number exercise

haskell/06-complex/complex.hs

@@ -3,30 +3,49 @@
 {-# HLINT ignore "Use void" #-}
 import Test.HUnit
 
-data Complex a = TODO
+data Complex a = Complex a a deriving (Eq)
 
-instance (Show a, Num a, Eq a) => Show (Complex a) where
-  -- show :: (Show a, Num a, Eq a) => Complex a -> String
-  -- TODO
+instance (Show a, Num a, Eq a, Ord a) => Show (Complex a) where
+  show (Complex re im)
+    | re == 0 && im == 0 = "0"
+    | re == 0 && im == 1 = "i"
+    | re == 0 && im == -1 = "-i"
+    | re == 0 = show im ++ "i"
+    | im == 0 = show re
+    | im == 1 = show re ++ "+i"
+    | im == -1 = show re ++ "-i"
+    | im > 0 = show re ++ "+" ++ show im ++ "i"
+    | otherwise = show re ++ show im ++ "i"
 
-instance (Num a, Floating a) => Num (Complex a) where
-  -- (+) :: (Num a, Floating a) => Complex a -> Complex a -> Complex a
-  -- (*) :: (Num a, Floating a) => Complex a -> Complex a -> Complex a
-  -- TODO
-  -- abs (Complex re im) = TODO
-  -- signum (Complex re im) = TODO
-  -- fromInteger n = TODO
-  -- negate :: (Num a, Floating a) => Complex a -> Complex a
-  -- negate (Complex re im) = Complex (negate re) (negate im)
+instance (Num a, Floating a, Eq a) => Num (Complex a) where
+  (Complex re1 im1) + (Complex re2 im2) = Complex (re1 + re2) (im1 + im2)
+  (Complex re1 im1) - (Complex re2 im2) = Complex (re1 - re2) (im1 - im2)
+  (Complex re1 im1) * (Complex re2 im2) = Complex (re1 * re2 - im1 * im2) (re1 * im2 + im1 * re2)
 
-instance (Fractional a, Floating a) => Fractional (Complex a) where
-  -- fromRational r = TODO
-  -- recip (Complex re im) = TODO
-    
-  -- (Complex re1 im1) / (Complex re2 im2) = TODO
+  abs (Complex re im) = Complex (sqrt (re * re + im * im)) 0
+  signum (Complex re im)
+    | re == 0 && im == 0 = Complex 0 0
+    | otherwise = let mag = sqrt (re * re + im * im) in Complex (re / mag) (im / mag)
 
--- conj :: Num a => Complex a -> Complex a
--- TODO
+  fromInteger n = Complex (fromInteger n) 0
+  negate (Complex re im) = Complex (negate re) (negate im)
+
+instance (Fractional a, Floating a, Eq a) => Fractional (Complex a) where
+  fromRational r = Complex (fromRational r) 0
+  recip (Complex re im) =
+    let denom = re * re + im * im
+     in Complex (re / denom) (negate im / denom)
+
+  (Complex re1 im1) / (Complex re2 im2) =
+    let denom = re2 * re2 + im2 * im2
+     in Complex ((re1 * re2 + im1 * im2) / denom) ((im1 * re2 - re1 * im2) / denom)
+
+conj :: (Num a) => Complex a -> Complex a
+conj (Complex re im) = Complex re (negate im)
+
+-- Imaginary unit
+i :: (Num a) => Complex a
+i = Complex 0 1
 
 tests :: Test
 tests =