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## Homework Statement

For each of the following functions f(z), find f'(z) and identify the maximal region for which f(z) is analytic.

1. [itex]f(z)=1/(z^2+1)[/itex]

2. [itex]f(z)=e^{-1/z}[/itex]

## Homework Equations

## The Attempt at a Solution

1. [itex]f'(z)=\frac{-2z}{(z^2+1)^2}[/itex]

*<--this part is easy. I'm having difficulty being certain of the maximum region for analyticity. Here is my attempt.*

f(z) is analytic everywhere but + or - i because f'(z) is undefined there.

*Is that a true stament or is the correct statement ...*f(z) is analytic everywhere but + or - i because f(z) is undefined there.

2. [itex]f'(z)=\frac{e^{-1/z}}{z^2}[/itex]

*<--this part is easy. I'm having difficulty being certain of the maximum region for analyticity. Here is my attempt.*

f(z) is analytic everywhere but 0 because f'(z) is undefined there. However, f(z) is analytic at infinity.

*Is that a true stament or is the correct statement ...*f(z) is analytic everywhere but 0 because f(z) is undefined there. However, f(z) is analytic at infinity.