I'm new on stack Exchange
I have a problem I think I can solve using Rouché's theorem But I have no idea how to start.
How should i show that $$f(z) = 5\sin(z) - e^z$$ has exactly 1 zero in the square with the origin as center and sides having length $\pi$?
Using Rouché's theorem, I should probably say that $$|5\sin(z)|<|e^z|$$ But I cant understand why.
Im so sorry for my bad english and probably stupid question But i cant figure it out myself
Thank you in advance :)