Here's the next one I could use some help on.

The principle argument of a complex number z, denoted by , is defined as the value of such that . Give an example of a complex sequence converging to a limit such that fails to converge.

I know of one such example:

This has a limit point of 0, but no well defined argument.

However the text says there is at least one other series with a limit point of -1. Not only have I been unable to construct an example (please help), but I can't see the logic behind this one at all. What is so special about -1 that, say, we can't construct one with a limit point of 1?

-Dan