diff --git a/src/Data/Aeson/Types/FromJSON.hs b/src/Data/Aeson/Types/FromJSON.hs
index 3f766e43..0f90efd8 100644
--- a/src/Data/Aeson/Types/FromJSON.hs
+++ b/src/Data/Aeson/Types/FromJSON.hs
@@ -93,6 +93,7 @@ import Data.Aeson.Types.Internal
 import Data.Aeson.Decoding.ByteString.Lazy
 import Data.Aeson.Decoding.Conversion (unResult, toResultValue, lbsSpace)
 import Data.Bits (unsafeShiftR)
+import Data.Complex (Complex(..))
 import Data.Fixed (Fixed, HasResolution (resolution), Nano)
 import Data.Functor.Compose (Compose(..))
 import Data.Functor.Identity (Identity(..))
@@ -1720,6 +1721,14 @@ instance (FromJSON a, Integral a) => FromJSON (Ratio a) where
             then fail "Ratio denominator was 0"
             else pure $ numerator % denominator
 
+instance FromJSON a => FromJSON (Complex a) where
+    parseJSON = withArray "Complex" $ \c ->
+        let n = V.length c
+        in if n == 2
+           then (:+) <$> parseJSONElemAtIndex parseJSON 0 c
+                     <*> parseJSONElemAtIndex parseJSON 1 c
+           else fail $ "cannot unpack array of length " ++ show n ++ "into a Complex"
+
 -- | This instance includes a bounds check to prevent maliciously
 -- large inputs to fill up the memory of the target system. You can
 -- newtype 'Scientific' and provide your own instance using
diff --git a/src/Data/Aeson/Types/ToJSON.hs b/src/Data/Aeson/Types/ToJSON.hs
index 7de88759..ce071c32 100644
--- a/src/Data/Aeson/Types/ToJSON.hs
+++ b/src/Data/Aeson/Types/ToJSON.hs
@@ -67,6 +67,7 @@ import Data.Aeson.Types.Internal
 import qualified Data.Aeson.Key as Key
 import qualified Data.Aeson.KeyMap as KM
 import Data.Bits (unsafeShiftR)
+import Data.Complex (Complex(..))
 import Data.DList (DList)
 import Data.Fixed (Fixed, HasResolution, Nano)
 import Data.Foldable (toList)
@@ -1421,6 +1422,16 @@ instance (ToJSON a, Integral a) => ToJSON (Ratio a) where
         "numerator" .= numerator r <>
         "denominator" .= denominator r
 
+instance ToJSON a => ToJSON (Complex a) where
+    toJSON (i :+ q) = Array $ V.create $ do
+        mv <- VM.unsafeNew 2
+        VM.unsafeWrite mv 0 (toJSON i)
+        VM.unsafeWrite mv 1 (toJSON q)
+        return mv
+    toEncoding (i :+ q) = E.list id
+        [ toEncoding i
+        , toEncoding q
+        ]
 
 instance HasResolution a => ToJSON (Fixed a) where
     toJSON = Number . realToFrac