Then the image formula_33 is a linear transformation, fixing the origin, and expressible as the action of a complex number of a particular type. When ("dx", "dy") is also interpreted as that type of complex number, the action is of complex multiplication in the appropriate complex number plane. As such, there is a type of angle (Euclidean, hyperbolic, or slope) that is preserved in such a multiplication. Due to "Df" being invertible, the type of complex number is uniform over the surface. Consequently, a surface deformation or diffeomorphism of surfaces has the conformal property of preserving (the appropriate type of) angles.