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Question Number 74914 by arkanmath7@gmail.com last updated on 03/Dec/19

C a n s o m e o n e s o l v e t h i s q u e s t i o n p l z ?

s o l v e t h e c o n t o u r i n t e g r a l

\int_{C} \frac{e^{i z}}{z^{3}} d z w h e r e C i s t h e c i r c l e ∣ z ∣= 2

Answered by mind is power last updated on 05/Dec/19

pols of f (z) = \frac{e^{iz}}{z^{3}} has pol at z = 0 order 3

\int \frac{e^{iz}}{z^{3}} dz = 2 i π Res (f, 0) = 2 i π . \frac{1}{2!} \frac{d^{2}}{{dz}^{2}} . z^{3} f (z) ∣_{z = 0}

= \frac{1}{2} 2 i π (- e^{iz}) ∣_{z = 0} = - i π

Commented by arkanmath7@gmail.com last updated on 04/Dec/19

t h i s q u s t . {i s n}^{'} t s o l v e d f r o m {S c h o u m}^{'} s a n d t h e

a n s w e r i s - π i

Commented by mind is power last updated on 05/Dec/19

yeah Res (f, 0) = \frac{1}{2!} \frac{d^{2}}{{dz}^{2}} z^{3} f (z) ∣_{z = 0}

Commented by arkanmath7@gmail.com last updated on 05/Dec/19

t h a n k y o u s i r

Commented by mind is power last updated on 05/Dec/19

y^{'} re welcom

we can generaliz it

\int_{C} \frac{e^{iz}}{z^{n}} dz = \frac{2 i π}{(n - 1)!} . {(i)}^{n - 1}

= \frac{2 π . {(i)}^{n}}{(n - 1)!}

Commented by arkanmath7@gmail.com last updated on 06/Dec/19

g o o d w o r k t h a n k s a g a i n