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Complex analysis limit

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that [tex]lim_{z \rightarrow 1+2i} [ix - (x+y)] = -3 + i[/tex].

    2. Relevant equations
    [tex]lim_{z \rightarrow z_0} f(z) = w_0[/tex] if and only if given [tex]\epsilon > 0[/tex] there exists a [tex]\delta > 0[/tex] such that [tex] 0 < |z-z_0| < \delta \Rightarrow |f(z)-w_0| < \epsilon[/tex]

    3. The attempt at a solution
    [tex]f(z) = ix-(x+y), w_0 = -3+i, z = x+iy, z_0 = 1+2i[/tex]

    I calculated the following:

    [tex]|z-z_0| = \sqrt{(x-1)^2+(y-2)^2}[/tex] and

    [tex]|f(z)-w_0| = \sqrt{(3-x-y)^2+(x-1)^2}[/tex]

    I need to somehow find a relationship between these, and this is where I'm struggling. Any help would be appreciated!
  2. jcsd
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