Well the result, which is

(%i4) diff(conjugate(z),q)-conjugate(diff(z,q)); d dz (%o4) -- (conjugate(z)) - conjugate(--) dq dq

is correct. Although the answer is indeed equal to zero mathematically, Maxima doesn't spot that.

To the developers: Maybe we should simplify `diff(conjugate(f(q)), q)`

to `conjugate(diff(f(q), q))`

? Arguments for: If f is differentiable, so is its conjugate; This creates a canonical form. Arguments against: How does one stop this happening? Yet another flag?