Answer to Question #236253 in Chemical Engineering for Loki

Question

20b)Use Cauchy integral formula for derivatives evaluate ∮c Sin 2πz/(z+1)² (z²+4)dz, where C is |z + 2| <2.

Explain the problem with step by step process?

Answer 1

$∮c z²-2z/(z+1)^2 (z²+4)dz$

$=∮𝐵(𝑖/2)1𝑧2+1𝑑𝑧=∮$

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

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

$=0$