calculate ∫_C (z/(z^2 +1))dz with C={z∈C/∣z∣=(1/2)}


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Question Number 37297 by math khazana by abdo last updated on 11/Jun/18
$calculate ∫_C (z/(z^2 +1))dz with C={z∈C/∣z∣=(1/2)}$
$c a l c u l a t e \int_{C} \frac{z}{z^{2} + 1} d z w i t h C = {z \in C / ∣ z ∣= \frac{1}{2}}$
Commented by math khazana by abdo last updated on 14/Jun/18

$l e t φ (z) = \frac{z}{z^{2} + 1} t h e p o l e s o f φ a r e i a n d - i$ $(a r e o u t o f t h e c i r c l e ∣ z ∣= \frac{1}{2}) \Rightarrow \int_{C} φ (z) d z = 0 \Rightarrow$ $\int_{C} \frac{z}{z^{2} + 1} d z = 0 .$
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