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Engineering Mathematics
Complex Functions

Practice questions from Complex Functions.

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Q#1 Complex Functions GATE EE 2025 (Set 1) NAT +2 marks -0 marks

Let  be a clockwise oriented closed curve in the complex plane defined by . Further, let  be a complex function, where . Then, __________ (round off to the nearest integer).

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Q#2 Complex Functions GATE EE 2024 (Set 1) MCQ +1 mark -0.33 marks

Which of the following complex functions is/are analytic on the complex plane?

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Q#3 Complex Functions GATE EE 2024 (Set 1) NAT +1 mark -0 marks

Consider the complex function . The coefficient of  in the Taylor series expansion of  about the origin is ________ (rounded off to 1 decimal place).

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Q#4 Complex Functions GATE EE 2021 (Set 1) MCQ +1 mark -0.33 marks

Let , where  is a complex number. Which one of the following is true?        

The complex roots of the equation  come in conjugate pairs.

All the roots cannot be real.

The sum of the roots of  is real number

Conjugate  conjugate  for all

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Q#5 Complex Functions GATE EE 2021 (Set 1) MCQ +2 marks -0.66 marks

Let  and  be the vertices of rectangle  in the complex plane. Assuming that  is traversed in counter-clockwise direction, the value of the contour integral  is

0

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Q#6 Complex Functions GATE EE 2020 (Set 1) MCQ +1 mark -0.33 marks

The value of the following complex integral, with  representing the unit circle centered at origin in the counterclockwise sense, is

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Q#7 Complex Functions GATE EE 2019 (Set 1) MCQ +1 mark -0.33 marks

Which one of the following functions is analytic in the region ?

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Q#8 Complex Functions GATE EE 2019 (Set 1) MCQ +2 marks -0.66 marks

The closed loop line integral

evaluated counter-clockwise, is

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Q#9 Complex Functions GATE EE 2018 (Set 1) MCQ +1 mark -0.33 marks

The value of the integral in counter clockwise direction around a circle C of radius 1 with centre at the point Z= -2 is

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Q#10 Complex Functions GATE EE 2018 (Set 1) MCQ +2 marks -0.66 marks

If C is a circle  and , then is

1

0

–1

–2

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Q#11 Complex Functions GATE EE 2017 (Set 1) MCQ +1 mark -0.33 marks

For a complex number  

–2i

–i

I

2i

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Q#12 Complex Functions GATE EE 2017 (Set 1) MCQ +2 marks -0.66 marks

Consider the line integral The line c is shown in the figure below

Z:\PY\EE\Redreaw figure\General ability-Sachin\979-12 (engineering natgs).jpg

The value of I is

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Q#13 Complex Functions GATE EE 2017 (Set 2) MCQ +2 marks -0.66 marks

The value of the contour integral in the complex-plane . Along the contour , taken counter-clockwise is

0

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Q#14 Complex Functions GATE EE 2016 (Set 1) MCQ +1 mark -0.33 marks

The value of the integral , over the contour, taken in the anti – clockwise direction, would be

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Q#15 Complex Functions GATE EE 2016 (Set 2) MCQ +1 mark -0.33 marks

Consider the function  where z is a complex variable and  denotes it complex conjugate. Which one of the following is TRUE?

f(z) is both continuous and analytic

f(z) is continuous but not analytic

(z) is not continuous but is analytic

f(z) is neither continuous nor analytic

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Q#16 Complex Functions GATE EE 2014 (Set 2) MCQ +1 mark -0.33 marks

All the values of the  multi – valued complex function , where , are

purely imaginary

real and non – negative

on the unit circle

equal in real and imaginary parts.

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Q#17 Complex Functions GATE EE 2014 (Set 3) MCQ +2 marks -0.66 marks

Integration of the complex function, in the counterclockwise direction, around, is

0

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Q#18 Complex Functions GATE EE 2013 (Set 1) MCQ +1 mark -0.33 marks

Square roots of –i, where            

i, –i

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Q#19 Complex Functions GATE EE 2013 (Set 1) MCQ +2 marks -0.66 marks

 Evaluated anticlockwise around the circle, where i =, is

-4π

0

2+π

2+2i

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Q#20 Complex Functions GATE EE 2012 (Set 1) MCQ +1 mark -0.33 marks

If , then the value of  is        

x

1

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Q#21 Complex Functions GATE EE 2012 (Set 1) MCQ +1 mark -0.33 marks

Given. If C is a counter clockwise path in the z-plane such that, the value of  is

-2

-1

1

2

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Q#22 Complex Functions GATE EE 2011 (Set 1) MCQ +1 mark -0.33 marks

A point z has been plotted in the complex plane, as shown in figure below.

18.jpg

The plot of the complex number  is

19.jpg

20.jpg

21.jpg

22.jpg

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Q#23 Complex Functions GATE EE 2007 (Set 1) MCQ +2 marks -0.66 marks

The value of   where C is the contour  is

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