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Test: Complex Variables - Engineering Mathematics MCQ


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15 Questions MCQ Test Engineering Mathematics - Test: Complex Variables

Test: Complex Variables for Engineering Mathematics 2026 is part of Engineering Mathematics preparation. The Test: Complex Variables questions and answers have been prepared according to the Engineering Mathematics exam syllabus.The Test: Complex Variables MCQs are made for Engineering Mathematics 2026 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 Engineering Mathematics for Engineering Mathematics & Test: Complex Variables solutions in Hindi for Engineering Mathematics course. Download more important topics, notes, lectures and mock test series for Engineering Mathematics Exam by signing up for free. Attempt Test: Complex Variables | 15 questions in 45 minutes | Mock test for Engineering Mathematics preparation | Free important questions MCQ to study Engineering Mathematics for Engineering Mathematics 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

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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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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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