Exercise 9. Explain why
9 (b). is
Solution 9 (b).
See text and/or instructor's solution manual.
, so that
, , , .
The Cauchy Riemann equations are
Hence we obtain and , which hold if and only if both and , which is impossible.
Therefore, is nowhere differentiable.
We are done.
reason why f(z) is not analytic is
given in Exercise 16 in Section
The complex form of the Cauchy-Riemann equations is .
The complex form of the Cauchy-Riemann equations fails to hold because .
This solution is complements of the authors.
(c) 2008 John H. Mathews, Russell W. Howell