The mapping u1 = e~ is confonnal throughout the entire:.

Chapter 0, Problem 9.1

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The mapping u1 = e~ is confonnal throughout the entire:. plane since (e;)' = e; i=- 0 for each:.. Consider any two lines .r =Ct and y = c1 in the :. plane. the first directed upv ... ard and the second directed to the 1ight. According to Example J in Sec. J 03. their images u1H.lcr che mapping w = e; arc a positively oriented circle centered at the origin and a my from the origin. respectively. As illustrated in Fig. J 24 (Sec. 103). the angle between the lines m their point of intersection is a right angle in the negative direction. and the same is true of the angle hctv .. een the circle and the ray at the corresponding point in the w plane. The con formality of the mapping w = ~ is also illustrated in Figs. 7 and 8 of Appendix 2.