Abstract
Abstract This chapter examines complex functions as transformations. A complex function f is a rule that assigns to a complex number z an image complex number w = f(z). In order to investigate such functions, it is essential that one is able to visualize them. Several methods exist for doing this, but the chapter focuses almost exclusively on the method introduced in the previous chapter. This means viewing z and its image w as points in the complex plane, so that f becomes a transformation of the plane. The chapter begins by looking at polynomials, power series, the exponential function, and cosine and sine. It then considers multifunctions, the logarithm function, and the process of averaging over circles.
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