Electronics and Communication Engineering
GATE ECE Complex Analysis PYQs
Build your understanding with focused practice from past exam papers.
How to practice Complex Analysis
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 13. Imported answers require independent review unless marked reviewed.
Question 36
Open questionECMCQ2 marksNeeds review
Consider the two series,
and
, where
Which of the following statements is correct for the two given series?
Your answerChoose one option.
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Open questionECMSQ2 marksNeeds review
Which of the following statements involving contour integrals (evaluated counter-clockwise) on the unit circle
in the complex plane is/are TRUE?Your answerSelect all correct options. You can choose more than one.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 43
Open questionECMCQ2 marksNeeds review
Let
be a complex variable. If
and
is the circle in the complex plane with
then
is ______.Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 13
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Let
. Which of the following cannot be a value of
?Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 14
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The value of the contour integral
, where the contour
is
, taken in the counter clockwise direction, isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 32
Open questionECNAT1 markNeeds review
A simple closed path
in the complex plane is shown in the figure. If
where
, then the value of
is ______ (rounded off to two decimal places). 
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 26
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Consider the integral
where
is a counter-clockwise oriented circle defined as
. The value of the integral isYour answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 1
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Which one of the following functions is analytic over the entire complex plane?
Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 16
Open questionECNAT1 markNeeds review
The value of the contour integral
evaluated over the unit circle
is ______.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 6
Open questionECMCQ1 markNeeds review
Consider p(s) = s³ + a₂s² + a₁s + a₀ with all real coefficients. It is known that its derivative p′(s) has no real roots. The number of real roots of p(s) is
Your answerChoose one option.
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