Chapter 14.9, Problem 14P

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 d s and angle arc tan $dy/dx)$ which is required to obtain the image of d z, namely dw.