# Homework Help: Limit in the complex plane

1. Feb 13, 2017

### cragar

1. The problem statement, all variables and given/known data
lim as z--> i , $\frac{z^2-1}{z^2+1}$
3. The attempt at a solution
When we plug in i we get -2/0, so we get division by 0, Does this mean the limit is
infinity, I also tried approaching from z=x+i where x went to 0, you get the same answer,
I also approached from z=yi where y approaches 1, and I got the same answer.

Last edited by a moderator: Feb 13, 2017
2. Feb 13, 2017

### Staff: Mentor

What happens with $\lim_{x \to 0} \frac 1 x$? Is the limit here $\infty$ or does the limit simply not exist at all? IOW, are the two one-sided limits equal?

3. Feb 13, 2017

### cragar

good point if we appraoch x from the left it goes to minus infinity , and if we approach from the right it is positive infinity, so the limit does not exist.