I'm starting to study complex numbers right now, and then I came across with this problem:
$$\frac{|z^m|}{|z^{n} +1|} < \frac{|R^m|}{|R^{n}-1|}$$ where $|z|=R$
I know that everything starts with triangle inequality, but I don't know how to continue the resolution. Can anyone help me? Any tips? Thank you very much!