Complex Variables and Partial Differential Equations (3130005)

Question-3a

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

Q3) (a)

Evaluate $\int_{C} \frac{1}{z^{2}} d z$ , Where $C : |z| = 1$ .

Evaluate

\int_{C} \frac{1}{z^{2}} d z

, Where

C : |z| = 1

.

\Rightarrow z_{0} = 0

is non analytic point in

C

,

f (z) = 1 & n = 1 .

But

f^{'} (z) = 0

.

→ Then by Cauchy's Integral formula,

\int_{C} \frac{1}{z^{2}} d z = \frac{2 πi}{n!} f^{n} (z_{0})

\Rightarrow \int_{C} \frac{1}{z^{2}} d z = \frac{2 πi}{1!} f^{1} (z_{0}) = 0

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