Existence of Limit of [(x+iy)/(x-iy)]^n

[kathrynag]

Homework Statement

For what values does the limit exist?
Lim_{n\rightarrow}\infty(\frac{z}{z conjugate})^n

Homework Equations

The Attempt at a Solution

[(x+iy)/(x-iy)]^n
I just don't know how to tell when it exists. For even values of n because then there would be no sign changes?

 

[Office_Shredder]

It should be obvious that the existence or non-existence of the limit depends on z (alternatively, x and y) not on n, since n is the argument for the limit (aside: is there a name for that?)