In this Section we consider two important features of complex functions. The Cauchy-Riemann equations provide a necessary and sufficient condition for a function f ( z ) to be analytic in some region of the complex plane; this allows us to find f ( z ) in that region by the rules of the previous Section.

A mapping between the z -plane and the w -plane is said to be conformal if the angle between two intersecting curves in the z -plane is equal to the angle between their mappings in the w -plane. Such a mapping has widespread uses in solving problems in fluid flow and electromagnetics, for example, where the given problem geometry is somewhat complicated.


Learning Outcomes

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