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4.5: Ejemplos
https://espanol.libretexts.org/Matematicas/Analisis/Variables_complejas_con_aplicaciones_(Orloff)/04%3A_Integrales_de_l%C3%ADnea_y_teorema_de_Cauchy/4.05%3A_Ejemplos
$\int_{\gamma} \dfrac{1}{z} \ dz = \int_{0}^{2\pi} \dfrac{1}{e^{i \theta}} ie^{i \theta} \ dt = \int_{0}^{2\pi} i \ dt = 2\pi i.$ (ii) Como es habitual, parametrizamos el círculo unitario como\(\gam... $\int_{\gamma} \dfrac{1}{z} \ dz = \int_{0}^{2\pi} \dfrac{1}{e^{i \theta}} ie^{i \theta} \ dt = \int_{0}^{2\pi} i \ dt = 2\pi i.$ (ii) Como es habitual, parametrizamos el círculo unitario como $\gamma (\theta = e^{i \theta}$ con $0 \le \theta \le 2\pi$ . $\int_{\gamma} \dfrac{1}{z^2} \ dz = \int_{0}^{2 \pi} \dfrac{1}{e^{2i \theta}} ie^{i \theta}\ d \theta = \int_{0}^{2\pi} i e^{-i \theta}\ d \theta = -e^{-i \theta} \vert_{0}^{2\pi} = 0.$

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