GATE MA Complex Analysis PYQs & Answers — Page 4

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Questions 31–40 of 54. Imported answers require independent review unless marked reviewed.

Topic practice 54 questionsPage 4 of 6

The number of zeroes (counting multiplicity) of

in the annular region

is __________.

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Consider the following statements:

is harmonic on

II:

has a harmonic conjugate on

Then

Your answerChoose one option.

both I and II are true

I is true but II is false

I is false but II is true

both I and II are false

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Let

and

be defined by

Suppose

and

are analytic functions. Consider the following statements:

is independent of paths

joining

and

II:

is independent of paths

joining

and

Then

Your answerChoose one option.

both I and II are true

I is true but II is false

I is false but II is true

both I and II are false

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Let

and let, for

If for a subset

denotes the closure of

, then

Your answerChoose one option.

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is a function such that

and its restriction to the unit circle is continuous, then

Your answerChoose one option.

is continuous but not necessarily analytic

is analytic but not necessarily a constant function

is a constant function

exists

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Suppose that

and

. If

, then the value of

is equal to

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and

, then

is equal to (correct up to one decimal place)

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Let

(the set of all complex numbers) be defined by

Let

denote the derivative of

with respect to

. Then which one of the following statements is TRUE?

Your answerChoose one option.

exists and

is analytic at the origin

is not differentiable at

is differentiable at

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Let

be any sequence of real numbers such that

. If the radius of convergence of

, then which one of the following statements is necessarily TRUE?

Your answerChoose one option.

is infinite

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Let

Then the greatest integer less than or equal to

is _____.

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GATE MA Complex Analysis PYQs

Question 48

Question 4

Question 5

Question 6

Question 36

Question 45

Question 46

Question 3

Question 10

Question 22