Pregunta: Utilizando la formula integral de Cauchy, calcular las integrales siguientes a. ∫∥z∥=1z2+2zezdz b. ∫∥z∥=5z2+16dz

a) Let $\mathrm{I}={\int }_{\Vert \mathrm{z}\Vert =1}\frac{{\mathrm{e}}^{\mathrm{z}}}{{\mathrm{z}}^2+2\mathrm{z}}\mathrm{d}\mathrm{z}$

$={\int }_{\mathrm{C}}\frac{{\mathrm{e}}^{\mathrm{z}}}{\mathrm{z}(\mathrm{z}+2)}\mathrm{d}\mathrm{z}$ where C=$\{\mathrm{z}\in \mathbb{C}:\Vert \mathrm{z}\Vert =1\}$is the circle with center at origin and radius 1.

Here the point z=0 lies...