Well if you want you can use the fact that
z= r exp(it) where r and t are real and then look on the real sequence of , where presumably you have proven it already in your real analysis course.
I am asked to prove that if then and
So I assume I have to treat these as sequence because cannot be a function of z since the n is there. I know the definition of the limit but I just get stuck. In were real I think I would take the log and proceed from there, but that seems considerably harder with the complex logarithm.
Anyway I have:
Let . Now I have to find a such that when , which I cannot do.
Can anyone help me... thanks.