Example 3.7.  At the beginning of this section (Equation (3-13)) we defined the function  

            .   

Show that this function is differentiable for all z, and find its derivative.

Explore Solution 3.7.

Enter the function f[z] and determine u[x,y] and v[x,y].

Verify that the Cauchy-Riemann equations hold.

We see that the Cauchy-Riemann equations hold.

Verify that  .  

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