calculate-C-z-z-2-1-dz-with-C-z-C-z-1-2-

Question Number 37297 by math khazana by abdo last updated on 11/Jun/18

c a l c u l a t e \int_{C} \frac{z}{z^{2} + 1} d z w i t h C = {z \in C / ∣ z ∣= \frac{1}{2}}

Commented by math khazana by abdo last updated on 14/Jun/18

l e t φ (z) = \frac{z}{z^{2} + 1} t h e p o l e s o f φ a r e i a n d - i

(a r e o u t o f t h e c i r c l e ∣ z ∣= \frac{1}{2}) \Rightarrow \int_{C} φ (z) d z = 0 \Rightarrow

\int_{C} \frac{z}{z^{2} + 1} d z = 0 .