GATE IN topic:complex-analysis PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 15. Imported answers require independent review unless marked reviewed.

Topic practice 15 questionsPage 1 of 2

Consider a function

where

is a complex variable. A simple closed contour

-plane encloses the point

The value of integral

______.

Your answerChoose one option.

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Consider the function

, where

is a complex variable. The sum of the residues at singular points of

is _____ (in integer).

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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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Let

be a complex variable and

be its complex conjugate. The equation

represents a

Your answerChoose one option.

parabola

hyperbola

ellipse

circle

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The complex functions

and

are both analytic in a given domain. Choose the correct option(s) from the following.

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

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, when expanded as a power series around

, would result in

, with the region of convergence (ROC)

. The coefficients

, are given by the expression__________.

Your answerChoose one option.

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Let

, where

denotes a complex number and

denotes

. The inverse function

maps the real axis to the________.

Your answerChoose one option.

unit circle with centre at the origin

unit circle with centre not at the origin

imaginary axis

real axis

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For the complex number

, where

and

. Which of the following statement(s) is/are true?

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

The phase is

The magnitude is 1

The magnitude is

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Consider the function

. The residue of

, is ______

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Let

be defined in the complex plane. The integral

over the contour of a circle

with center at the origin and unit radius is ____.

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GATE IN topic:complex-analysis PYQs

How to practice topic:complex-analysis

Question 13

Question 33

Question 49

Question 11

Question 49

Question 19

Question 39

Question 50

Question 61

Question 24