GATE MA topic:complex-analysis PYQs & Answers — Page 3

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topic:complex-analysis

Questions 21–30 of 54. Imported answers require independent review unless marked reviewed.

Topic practice 54 questionsPage 3 of 6

Let

be an open connected subset of

containing

. Let

. Consider the following statements:

: There exists

such that

for all

, where

denotes the third derivative of

Then

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

is TRUE

is FALSE

is TRUE

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Consider the real function of two real variables given by

Let

be the harmonic conjugate of

such that

. Let

and

, then the value of

Your answerChoose one option.

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The value of the integral

where

is the circle of radius 2 centred at the origin taken in the anti-clockwise direction is

Your answerChoose one option.

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The radius of convergence of the series

is ________ (round off to TWO decimal places).

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The number of zeros of the polynomial

in the unit disc

is ________.

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Let

be a Möbius transformation such that

and

, where

. Let

denote the straight line passing through the origin with slope

, and let

denote the circle of unit radius centred at the origin. Then, which of the following statements are TRUE?

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

maps

to a straight line

maps

to a circle

maps

to a straight line

maps

to a circle

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Let

for

, where

and

are real numbers, be a non-constant analytic function on the complex plane

. Let

and

denote the first order partial derivatives of

and

with respect to real variables

and

, respectively. Consider the following two functions defined on

Then

Your answerChoose one option.

both

and

are analytic in

is analytic in

and

is NOT analytic in

and

is analytic in

neither

nor

is analytic in

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Let

, be the Möbius transformation which maps the points

in the

-plane onto the points

in the

-plane, respectively. Then the image of the set

under the map

Your answerChoose one option.

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Let

and

be the positively oriented boundary of

. Then the value of the integral

is __________.

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Let

and

be the function defined by

for

, then

__________.

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GATE MA topic:complex-analysis PYQs

Question 43

Question 13

Question 14

Question 28

Question 29

Question 50

Question 2

Question 3

Question 46

Question 47