13.7 Logarithm. General Power. Principal Value
The main feature of conformal mappings is that they are
angle-preserving (except at some critical points) and allow a
geometric approach to complex analysis. More details are as
follows. Consider a complex function defined in a domain D of
the z–plane; then to each point in D there corresponds a point
in the w-plane. In this way we obtain a mapping of D onto the
range of values of in the w-plane. In Sec. 17.1 we show that if
f(z) is an analytic function, then the mapping given by is a
conformal mapping, that is, it preserves angles, except at
points where the derivative is zero. (Such points are called
critical points.)