diff --git a/cayley-dickson.cabal b/cayley-dickson.cabal
--- a/cayley-dickson.cabal
+++ b/cayley-dickson.cabal
@@ -1,5 +1,5 @@
 name:                cayley-dickson
-version:             0.1.3.0
+version:             0.1.4.0
 synopsis:            Complex numbers, quaternions, octonions, sedenions, etc.
 description:         Cayley-Dickson constructions (complex numbers, quaternions,
                      octonions, sedenions, etc.) over general scalars without
@@ -9,7 +9,7 @@
 author:              James M. Lawrence
 maintainer:          James M. Lawrence <llmjjmll@gmail.com>
 copyright:           Copyright (c) James M. Lawrence
-category:            Algebra, Data, Data Structures, Math
+category:            Algebra, Math
 build-type:          Simple
 extra-source-files:  README.md
 cabal-version:       >=1.10
diff --git a/src/Math/CayleyDickson.hs b/src/Math/CayleyDickson.hs
--- a/src/Math/CayleyDickson.hs
+++ b/src/Math/CayleyDickson.hs
@@ -260,11 +260,13 @@
 polar :: (Tag n, Conjugable a, RealFloat a) => Nion n a -> (a, a, Nion n a)
 polar = polar' Proxy
 
-applyUsing :: (Conjugable a, RealFloat a) =>
-              Nion n a -> (a -> a) -> (C.Complex a -> C.Complex a) ->
-              Nion n a -> Nion n a
-applyUsing _ f _ (Scalar s) = Scalar $ f s
-applyUsing sqrtMinus1 _ f z = x .+ u *. y
+applyUsing' :: (Tag n, Conjugable a, RealFloat a) =>
+               Proxy n ->
+               Nion n a -> (a -> a) -> (C.Complex a -> C.Complex a) ->
+               Nion n a -> Nion n a
+applyUsing' n sqrtMinus1 fr f z
+  | tagVal n == 0 = Scalar $ fr $ scalarPart z
+  | otherwise = x .+ u *. y
   where (s, t, u) = polarUsing sqrtMinus1 z
         -- handle special cases for a little more accuracy
         x C.:+ y | t == 0 = f s'
@@ -273,6 +275,11 @@
                  where s' = s C.:+ 0
                        t' = t C.:+ 0
                        u' = 0 C.:+ 1
+
+applyUsing :: (Tag n, Conjugable a, RealFloat a) =>
+              Nion n a -> (a -> a) -> (C.Complex a -> C.Complex a) ->
+              Nion n a -> Nion n a
+applyUsing = applyUsing' Proxy
 
 ----------------------------------------------------------
 -- constants
diff --git a/test/test.hs b/test/test.hs
--- a/test/test.hs
+++ b/test/test.hs
@@ -244,9 +244,11 @@
            nion [1 % 2, 1, 3 % 2, 2] 
 
   forM_ [-2, -1, -0.5, 0, 0.5, 1, 2] $ \r -> do
-    let (s, t, u) = polar $ (fromScalar r :: Quaternion Double)
+    let y = fromScalar r :: Quaternion Double
+        (s, t, u) = polar y
     assert $ s >= 0
     assertClose (fromScalar r) $ s .* exp (t .* u)
+    assertClose (sqrt y) $ (sqrt s) .* exp ((t .* u) /. 2)
 
 checkInverses :: IO ()
 checkInverses = do