1550251515-Classical_Complex_Analysis__Gonzalez_

Elementary Functions 239

Fig. 5.11

q

Fig. 5.12

rotation 0, and forming an angle^1 / 2181 (Fig. 5.12), z being on the bisector

of the angle.

Also, a homotecy w = Rz is equivalent to the product of two symmetries

(inversions) with respect to two concentric circles with center at 0 and

radii r 1 , r 2 such that rz/r 1 = R^112 (Fig. 5.13). Summing up, we see that

W=Z"=RZ

Fig. 5.13