So I understand how to show that there is no solutions, but my lecturer said before that, I must show that for allSuppose that a function that is analytic in some arbitrary region Ω in the complex plane containing the interval [1,1.2]. Assume for all . Show that has no solutions in Ω.

I'm not sure how to explain it. There are some theorems that say if (for z on some interval) has an accumulation point a the origin then for all z in the complex plane, but this equation has no accumulation point at the origin.

So how do I go about showing f(z) = cot(z) for all z, instead of just the small interval given?