Question

12)Use Cauchy integral formula for derivatives evaluate ∮c z²-2z/(z+1)^2 (z²+4)dz, where C is |z + 2) <2.

Answer 1

$∮c z²-2z/(z+1)^2 (z²+4)dz$

$=∮𝐵(𝑖/2)1𝑧2+1𝑑𝑧=∮$

$=∮_{B2}{i/2} (1/2i)/(z+1)^2 dz-\oint_{B2}$

$=\frac{1}{2i}-\frac{1}{2i}$

$=0$