[Haskell] type inference & instance extensions

[Doug McIlroy]

A fragment of an attempt to make pairs serve as complex numbers,
using ghc/hugs extensions:

        instance Num a => Num (a,a) where
                (x,y) * (u,v) = (x*u-y*v, x*v+y*u)

Unfortunately, type inference isn't strong enough to cope with

        (1,1)*(1,1)

Why shouldn't it be strengthened to do so?
Or is there a declarative trick (perhaps with dependent
classes) that will accomplish the goal?

Doug McIlroy