GATE MA Complex Analysis PYQs & Answers

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Questions 1–10 of 54. Imported answers require independent review unless marked reviewed.

Topic practice 54 questionsPage 1 of 6

Let

be defined by

. Which one of the following is TRUE?

Your answerChoose one option.

is differentiable at

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Let

denote the unit disc in the complex plane

. Let

be an analytic function which satisfies

. Then which one of the following is a possible value of

Your answerChoose one option.

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For

, the power series

converges at

and diverges at

. Then the radius of convergence of this power series is equal to ________. (answer in integer)

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The value of the contour integral

, where

, oriented in the counter-clockwise direction, is equal to

Your answerChoose one option.

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Let

. On which one of the following domains, does

represent an analytic function?

Your answerChoose one option.

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Let

and

be two Möbius transformations defined on the unit disc

. Consider the following statements:

;

. Which of the following statements is/are CORRECT?

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

is true.

is true and

is false.

Neither

is true nor

is true.

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The number of zeros of the complex polynomial

in the annulus

is equal to ________. (answer in integer)

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Consider

where

is oriented positively as a simple closed curve. Then, the value of

is equal to _____ (in integer)

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Let

be the Möbius transformation that maps the points

and

conformally onto the points

and

, respectively, in the extended complex plane. If

maps the circle centred at

with radius

onto a straight line given by the equation

, then the value of

is equal to

Your answerChoose one option.

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Let

and

, where

denotes the imaginary part of

. Let

be the set of all bijective analytic functions

such that

. Then, the value of

Your answerChoose one option.

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GATE MA Complex Analysis PYQs

How to practice Complex Analysis

Question 17

Question 18

Question 35

Question 38

Question 39

Question 50

Question 59

Question 33

Question 41

Question 42