Complex Analysis

“ca: ch_02” — 2012/3/27 — 19:14 — page 43 — #3

Analytic Functions

|

43

then point P



(w) will move along a corresponding curve C



in the w-plane since to each point

z =(x, y), there corresponds a point w =(u, v). We say that the function w = f (z) thus defines a

mapping or transformation of the z-plane into the w-plane and the curve C in the z-plane is mapped or

transformed into the curve C



into the w-plane by transformation. We call P



(w) the image of P(z), i.e.

the image of a point z in the domain of definition S is the point w = f (z). If M ⊆S, then the set of image

of all points in the set M is the image of M. The set R ={f (z) : z ∈ S} of the image ...