2. (20 pts) evaluate (a) ∫|z|=1 √9 - z 2dz; (b) ∫|z|=2 (z + 1) -2e zdz

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2. (20 pts) evaluate (a) ∫|z|=1 √9 - z 2dz; (b) ∫|z|=2 (z + 1) -2e zdz; (c) ∫|z-2i|=2 (z - i) -3arcsin zdz; (d) ∫|z|=2 z 3 (z - 1) -4dz; (e) let γ = [-1,1 + i] + β + [-1 + i, 1] where β(t) = i + e it for 0 ≤ t ≤ 3π. compute ∫γ (z 2 + 1) -1dz

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(20 pts) Evaluate
(a) $\int_{| z | = 1} \sqrt{9 - z^{2}} d z$ ;
(b) $\int_{| z | = 2} (z + 1)^{- 2} e^{z} d z$ ;
(c) $\int_{| z - 2 i | = 2} (z - i)^{- 3} Arcsin z d z$ ;
(d) $\int_{| z | = 2} z^{3} (z - 1)^{- 4} d z$ ;
(e) Let $γ = [- 1, 1 + i] + β + [- 1 + i, 1]$ where $β (t) = i + e^{i t}$ for $0 \leq t \leq$
$3 π$ . Compute $\int_{γ} {(z^{2} + 1)}^{- 1} d z$ ;