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Limit of exp(z) (complex number)

  1. Jul 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Find limit as z->infinity of exp(z) where z is complex

    2. Relevant equations

    See above

    3. The attempt at a solution

    The solution should be that the limit does not exist, but I don't know why. Any explanations?
  2. jcsd
  3. Jul 1, 2009 #2


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    Put z=iy, where y is real. Now let y->infinity.
  4. Jul 1, 2009 #3
    Is it because e^iy = r(cos(y)+i*sin(y)) and that equation simply oscillates and never goes to infinity no matter how large y gets?
  5. Jul 1, 2009 #4


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    Right, if you put r=1. Or consider z=x and z=(-x) for x real and let x->+infinity. One limit is infinity, and the other is zero. There is no definite single limit as z->infinity. Consider definite cases of z->infinity to get a feeling for what's going on.
  6. Jul 1, 2009 #5
    Thanks a lot got it figured out
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