haskell - Typeclasses for overloading division -

i'm defining own complex number data type learning exercise, , i've run trouble overloading (/) operator. seems can't include in instance of floating or fractional, compiler saying (/) isn't visible method of classes. there (preferably numeric) typeclass allow me overload operator? eg.

instance someclass => someclass (complex a)     (/) b@(complex r i) = fmap (/(r^2 - i^2)) (a * (conjugate b)) 

here's current implementation implementation interested:

module complex data complex = complex {real :: a, imaginary :: a}  = complex 0 1  instance num => show complex     show (complex r i)         | < 0 = show r ++ " - i" ++ show (negate i)         | otherwise = show r ++ " + i" ++ show  instance functor complex     fmap f (complex r i) = complex (f r) (f i)  instance num => num (complex a)     (+) (complex ra ia) (complex rb ib) = complex (ra + rb) (ia + ib)     (-) (complex ra ia) (complex rb ib) = complex (ra - rb) (ia - ib)     (*) (complex ra ia) (complex rb ib) = complex (ra*rb - ia*ib) (ra*ib + rb*ia)  instance floating => floating (complex a)     (/) b@(complex r i) = fmap (/(r^2 - i^2)) (a * (conjugate b))  conjugate :: num => complex -> complex conjugate (complex r i) = complex r (negate i) 

when type :t (/) in ghci, obtain:

(/) :: fractional => -> -> 

so means member of fractional, not floating. can rewrite to:

instance fractional => fractional (complex a)     (/) b@(complex r i) = fmap (/(r^2 - i^2)) (a * (conjugate b))

and since nitpicking, have add brackets show instance:

instance num => show (complex a)     show (complex r i)         | < 0 = show r ++ " - i" ++ show (negate i)         | otherwise = show r ++ " + i" ++ show i