ABSTRACT
This chapter is concerned with questions that have a geometric, qualitative nature rather than an analytical, quantitative one. These questions center around the issue of the local geometric behavior of a holomorphic function. It discusses the ways to locate the zeros of a holomorphic function and to divide up the complex line integral. The argument principle is both useful and important. The argument principle for meromorphic functions is provided with a set of corresponding exercises. The argument principle for holomorphic functions has a consequence that is one of the most important facts about holomorphic functions considered as geometric mappings. A typical application of Rouche’s Theorem and the fundamental theorem of algebra are discussed with examples.
