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Answered Same Day Dec 20, 2021

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David answered on Dec 20 2021

117 Votes

As C is analytic closed curve. Hence, without loss of generality, we can
assume that C is unit circle. That is
C = {z : |z| = 1} = {eiθ : 0 ≤ θ < 2π}
Now for 0 < � < 12 , Let
Ω = {z : 1− � < |z| < 1 + �}.
Then we have C ⊂ Ω.
Define
f : Ω→ C
y f(z) =
1
z
.
As 0 /∈ Ω, we see that f is...

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