Does the Limit in the Complex Plane Approach Infinity?

[cragar]

Homework Statement

lim as z--> i , \frac{z^2-1}{z^2+1}

The Attempt at a Solution

[/B]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.

 

[Mark44]

Homework Statement

lim as z--> i , \frac{z^2-1}{z^2+1}

The Attempt at a Solution

[/B]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.

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?

 

[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.