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The problem statement, all variables and given/known data

Find the limit of each function at the given point or explain why it does not exist.

(a) f(z) = (1 - Im z)^{-1}at 8 + i

(b) f(z) = (z - 2) log |z - 2| at 2

The attempt at a solution

(a) f(z) is a real valued function and it seems to me that it approaches infinity as z approaches 8 + i. The book states the limit doesn't exist. I don't get it.

(b) This one is also real valued. Can I safely apply l'Hospital's rule? I'm worried because of log |z - 2|. I know |z - 2| is not differentiable at 2 but since I'm taking a limit, I need not worry right? I get that the limit is 0. Is there another way to evaluate the limit without l'Hospital's rule or using power series?

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# Homework Help: Checking Some Complex Limits

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