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
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
(And a correction of a minor typo in red).