1.

Evaluate ∫c (z/(z - 2))dz where c is a circle |z| = 1.

Answer»

Let f(z) = z/(z - 2)

z = 2 lies outside c. 

∴ f(z) is analytic inside and on c . 

f'(z) is continuous inside c 

Hence by Cauchy’s theorem R c f(z)dz = 0



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