I understand how the equations work but i can't seem to be able to determine whether "1 / (1 + z)" satisfies the cauchy-riemann equations and hence determine whether f ' (z) exists.

Any help would be greatly apprichiated

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- December 21st 2009, 04:44 AMjezzyjezCauchy-Riemann equations
I understand how the equations work but i can't seem to be able to determine whether "1 / (1 + z)" satisfies the cauchy-riemann equations and hence determine whether f ' (z) exists.

Any help would be greatly apprichiated - December 21st 2009, 04:49 AMmr fantastic
- December 21st 2009, 05:13 AMjezzyjez
Yeh cool i get that now thanks, am i missing a trick with the last part of the question

"determine whether f ' (x) exists"

or does it literally exist when the equations satisfy the C-R equations?? - December 21st 2009, 05:23 AMtonio

You can evaluate the partial derivatives with the function as Mr. Fantastic showed you, or else realize (most books have it) that the CR-equations

are equivalent to , where we have that , so putting , we get:

.

Check the above and conclude your function is analytic in

Tonio - December 21st 2009, 08:13 PMmr fantastic
A thread of related interest: http://www.mathhelpforum.com/math-he...erivation.html

(And a correction of a minor typo in red). - December 21st 2009, 09:14 PMBruno J.