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Homework Help: Complex Limits

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations



    3. The attempt at a solution
    Not to sure how to go about this question?
     
  2. jcsd
  3. Mar 17, 2012 #2
    Write it out with z=x+iy.
     
  4. Mar 17, 2012 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Take the limit approaching 0 along the real axis and along the imaginary axis. Show that the results are different.
     
  5. Mar 17, 2012 #4
    I have come up with this

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

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