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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Tests  >  GATE ECE (Electronics) Mock Test Series 2025  >  Test: Complex Variables - Electronics and Communication Engineering (ECE) MCQ

Test: Complex Variables - Electronics and Communication Engineering (ECE) MCQ


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15 Questions MCQ Test GATE ECE (Electronics) Mock Test Series 2025 - Test: Complex Variables

Test: Complex Variables for Electronics and Communication Engineering (ECE) 2024 is part of GATE ECE (Electronics) Mock Test Series 2025 preparation. The Test: Complex Variables questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Complex Variables MCQs are made for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Complex Variables below.
Solutions of Test: Complex Variables questions in English are available as part of our GATE ECE (Electronics) Mock Test Series 2025 for Electronics and Communication Engineering (ECE) & Test: Complex Variables solutions in Hindi for GATE ECE (Electronics) Mock Test Series 2025 course. Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free. Attempt Test: Complex Variables | 15 questions in 45 minutes | Mock test for Electronics and Communication Engineering (ECE) preparation | Free important questions MCQ to study GATE ECE (Electronics) Mock Test Series 2025 for Electronics and Communication Engineering (ECE) Exam | Download free PDF with solutions
Test: Complex Variables - Question 1
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The integration of f (z) = x2 + ixy from A(1, 1) to B(2, 4) along the straight line AB joining the two points is

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x = at + b, y = ct + d

Test: Complex Variables - Question 2
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​ ​ ​

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We know by the derivative of an analytic function that

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Test: Complex Variables - Question 3
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Test: Complex Variables - Question 4
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Let f (z) = cosπz then f(z) is analytic within and on |z| =3, now by Cauchy’s integral formula

Test: Complex Variables - Question 5
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Test: Complex Variables - Question 6
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The value of    around a rectangle with vertices at   is
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Test: Complex Variables - Question 7
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  where c is the circle x2 + y2 = 4

Que: The value of f(3) is
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Test: Complex Variables - Question 8
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  where c is the circle x2 + y2 = 4

Que: The value of f' (1 - i) is
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The point (1 - i) lies within circle |z| = 2 ( ... the distance of 1 - i i.e., (1, 1) from the origin is √2 which is less than 2, the radius of the circle).

Let Ø(z) = 3z2 + 7z + 1 then by Cauchy’s integral formula

Test: Complex Variables - Question 9
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Expand the given function in Taylor’s series.

Que: 

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Test: Complex Variables - Question 10
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Expand the given function in Taylor’s series

Que: 
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Test: Complex Variables - Question 11
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Expand the given function in Taylor’s series.

Que: 
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Test: Complex Variables - Question 12
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If |z + 1|  < 1, then z-2 is equal to
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Test: Complex Variables - Question 13
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Expand the function   in Laurent’s series for the condition given in question.

Que: 1 < |z| < 2
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Test: Complex Variables - Question 14
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Expand the function   in Laurent’s series for the condition given in question.

Que: |z| > 2 
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Test: Complex Variables - Question 15
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The value of the integral 
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Cauchy's integral formula: Let f(z) be a complex analytic function within and on a closed contour C inside a simply-connected domain, and if a is any point in the middle of C, then

Explanation:

Here C: |1 - z| = 1
The singularities of are z2 = 1 i.e., z = ± 1 out of which z = 1 lies inside C.
So, f(z) = 
Then using Cauchy's integral formula

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Important Questions for Complex Variables

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Complex Variables MCQs with Answers

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