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Limit in the complex plane

  1. Feb 13, 2017 #1
    1. The problem statement, all variables and given/known data
    lim as z--> i , [itex] \frac{z^2-1}{z^2+1} [/itex]
    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. jcsd
  3. Feb 13, 2017 #2


    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?
  4. Feb 13, 2017 #3
    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.
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