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Test: Complex Variables - Civil Engineering (CE) MCQ


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15 Questions MCQ Test Engineering Mathematics - Test: Complex Variables

Test: Complex Variables for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: Complex Variables questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Complex Variables MCQs are made for Civil Engineering (CE) 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 Engineering Mathematics for Civil Engineering (CE) & Test: Complex Variables solutions in Hindi for Engineering Mathematics course. Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Attempt Test: Complex Variables | 15 questions in 45 minutes | Mock test for Civil Engineering (CE) preparation | Free important questions MCQ to study Engineering Mathematics for Civil Engineering (CE) Exam | Download free PDF with solutions
Test: Complex Variables - Question 1

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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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

  where c is the upper half of the circle z = 1

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Given contour c is the circle |z| = 1

Test: Complex Variables - Question 5

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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 6

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Test: Complex Variables - Question 7

The value of    around a rectangle with vertices at   is

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Test: Complex Variables - Question 8

  where c is the circle x2 + y2 = 4

Que: The value of f(3) is

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Test: Complex Variables - Question 9

  where c is the circle x2 + y2 = 4

Que: The value of f' (1 - i) is

Detailed Solution for Test: Complex Variables - Question 9

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 10

Expand the given function in Taylor’s series.

Que: 

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Test: Complex Variables - Question 11

Expand the given function in Taylor’s series

Que: 

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Test: Complex Variables - Question 12

Expand the given function in Taylor’s series.

Que: 

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Test: Complex Variables - Question 13

If |z + 1|  < 1, then z-2 is equal to

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Test: Complex Variables - Question 14

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 15

Expand the function   in Laurent’s series for the condition given in question.

Que: |z| > 2 

Detailed Solution for Test: Complex Variables - Question 15

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