# Homework Help: Complex Limits

1. Mar 17, 2012

### Rubik

1. The problem statement, all variables and given/known data

Show that the lim z→0 of (z/$\bar{z}$)2 does not exist

2. Relevant equations

3. The attempt at a solution

2. Mar 17, 2012

### micromass

Write it out with z=x+iy.

3. Mar 17, 2012

### HallsofIvy

Take the limit approaching 0 along the real axis and along the imaginary axis. Show that the results are different.

4. Mar 17, 2012

### Rubik

I have come up with this

Taking the limit along the Real axis:
lim as z→0 of (z/$\bar{z}$)2
= lim (x + 0i)2/(x - 0i)2
= lim x2/x2
= 1

Then taking the limit at the points x + xi for x→0:
lim as z→0 of (z/$\bar{z}$)2
= lim (x + xi)2/(x - xi)2
= lim (2x2)/(-2x2)
= -1

and since 1 ≠ -1 The limit does not exist.