Problem 1. Consider a holomorphic function f : U - V = f(U) on a domain U c C. Let zo E U, and let wo = f(zo) E V be its image. Consider two smooth curves a c U and B c V shown in Figure 1. Note that the former goes through zo, and the latter goes through wo. In each of the following cases, sketch i) what f(a) looks like in a small neighborhood Ne(wo) of wo; and ii) what f-(8) looks like in a small neighborhood Ne(zo) of zo. a) f'(zo) = 1 + V3i, f"(zo) =0, and f"(zo) = 1 - V2i. b) f'(zo) = 0, f"(zo) = -V8 - V8i, and f"(zo) = 3i. c) f'(zo) = 0, f"(zo) = 0, and f"(zo) = 3i. Figure 1 V C U wo to V C U K wo 170