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[SOLVED] Checking Some Complex Limits
Homework Statement
Find the limit of each function at the given point or explain why it does not exist.
(a) f(z) = (1 - I am 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?
Homework Statement
Find the limit of each function at the given point or explain why it does not exist.
(a) f(z) = (1 - I am 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?