Example 10.1.  Show that the mapping    is conformal at the points , , and , and determine the angle of rotation given by at the given points.

Explore Solution 10.1.

Enter the function f(z) = cos(z).

(a) Consider the mapping  w = cos(z)  near .

The image of a small rectangle about    is a curvilinear region about .

(b) Consider the mapping  w = cos(z)  near .

The image of a small rectangle about   is a curvilinear region about .  

(c) Consider the mapping  w = cos(z)  near .

The image of a small rectangle about    is a curvilinear region about  .  

(d) Consider the mapping  w = cos(z)  near .

The image of a small rectangle about  z = 1- i  is a curvilinear region about .  

(c) 2006 John H. Mathews, Russell W. Howell