GATE IN 2025 IN Q49: Analysis of complex variables

Choose the correct statement(s) from the following options, regarding Cauchy’s theorem on complex integration

where C is a simple closed path in a simply connected domain D.

Your answerSelect all correct options. You can choose more than one.

Cauchy’s theorem cannot be directly applied to conclude that

when

, and C is the unit circle

is analytic in D, then it can be concluded that

for any simple closed path C in D

The function

must be analytic in D to conclude

for any simple closed path C in D

when

, since the function is not analytic at

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