I couldn't tackle these two problems. if you don't mind, could you help for these exercises... thanks for everything.
nfie the oriented angle between two curves passing through a point in the complex plane. Show that an analytic function with non zero derivative preserves oriented angles.
be a domain in the complex plane and suppose that f is an analytic function on
Show that the function g de
is analytic in the domain
You should be able to find the proof of 1 in any good complex analysis book at all.
For the second one, I think you mean
can you confirm this?
If that's the case then, it's easy, just look at the power series and use the Cauchy-Hadamard theorem plus the fact that
is analytic on