Complex Variables and Partial Differential Equations (3130005)

Question-2c(i)

BE | Semester-3 Summer-2020 | 27-10-2020

Q2) (c(i))

Evaluate $\int_{C} \frac{e^{- z}}{z + 1} d z$ ,where $C : |z| = \frac{1}{2}$ .

Here, f (z) = \int_{C} \frac{e^{- z}}{z + 1} d z

\Rightarrow z_{0} = - 1

is a non-analytic point. But it is outside of

C : |z| = \frac{1}{2} .

\Rightarrow f (z)

is analytic in

C

.

Then by Cauchy’s integral theorem, We have,

\int_{C} \frac{e^{- z}}{z + 1} d z = 0

.

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