- #1

looserlama

- 30

- 0

## Homework Statement

Let z

_{n}= Arg(-1 + i/n). Find lim

_{n→∞}z

_{n}

## Homework Equations

Definition of convergence of a sequence.

## The Attempt at a Solution

Well z

_{n}= Arg(-1 + i/n) = arctan(-1/n).

So it seems clear that lim

_{n→∞}arctan(-1/n) = arctan(lim

_{n→∞}-1/n) = arctan(0) = [itex]\pi[/itex].

Which is true if arctan is continuous.

There's the problem, I don't know how to prove that arctan is continuous. It seems way more difficult that I expected. I can't seem to get anywhere with it.

How do you show it?

Or can anyone think of another way to find the limit?