_{D z z. Z γ f(z) dz = 0 . Proof. Z γ f(z) dz = Z D ∂f ∂z dz ∧ dz = 0 Corollary 1.3 (Cauchy’s Integral formula) f ∈ Cω(D), D simply connected, γ = δD. For any a ∈ D f(a) = 1 2πi Z γ f(w) dw w −a. Proof. Deﬁne for small enough ǫ > 0 the set Dǫ = D \{|z −a| ≤ ǫ} and the curve γǫ: t → z +ǫeit. (Because D isWeb }

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