We have discussed the fact that a conformal transformation magnifies and rotates an infinitesimal geometrical figure. We showed that ∣dw/dz∣ is the magnification factor. Show that the angle of dw/dz is the rotation angle. Hint: Consider the rotation and magnification of an arc dz=dx+idy (of length ds and angle arctandy/dx) which is required to obtain the image of dz, namely dw.