Jacobian works fine, though, so FiniteDifferences can do it, it just refuses to reshape the answer into a convenient format for some reason:
julia> fdm = central_fdm(5, 1);
julia> z = randn(ComplexF64)
0.20329027967321606 - 0.33123337931888125im
julia> jacobian(fdm, x -> z*x, randn())[1]
2×1 Matrix{Float64}:
0.20329027967321567
-0.3312333793188763
julia> jacobian(fdm, x -> z*x, randn(ComplexF64))[1]
2×2 Matrix{Float64}:
0.20329 0.331233
-0.331233 0.20329
Jacobian works fine, though, so
FiniteDifferencescan do it, it just refuses to reshape the answer into a convenient format for some reason: