Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download
Q. 1 Given 
the value of the definite integral
[2015 : 1 Mark, Set-II]
(a) 1
(b) -1
(c) i
(d) - i
Ans: c
Q. 2 Consider the following complex function
Which of the following is one of the residues of the above function ?
[2015 : 2 Marks, Set- 1]
(a) -1
(b) 9/16
(c) 2
(d) 9
Ans: a
f(z) has poles at z = 1, - 2 Residue of f(z ) at ( z = 1)
Residue of f(z) at ( z = -2 )
Q. 3 
can be expressed as
(a) - 0.5 - 0.5i
(b) - 0.5 + 0.5i
(c) 0.5 - 0.5i
(d) 0.5 + 0.5i [2014 : 1 Mark, Set-II]
Ans: (b)
Q. 4 For an analytic function, f{x; + iy) = u(x, y) + iv[x, y), u is given by u = 3x2- 3y2 . The expression for v, considering K to be a constant is
(a) 3 y2 - 3x2 + K
(b) 6x - 6 y + K
(c) 6y - 6x + K
(d) 6xy + K [2011 : 2 Marks]
Ans (d)
f= u + iv
u = 3x2 - 3y2
For f to be analysis, we have Cauchy-Riemann conditions,
From (i) we have,
Now applying equation (ii) we get,
Substitute in equation (iii),
The document Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)
FAQs on Complex Functions - Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
| 1. What are complex functions? |  |
Ans. Complex functions are functions that take complex numbers as inputs and produce complex numbers as outputs. They can be expressed as f(z) = u(x, y) + iv(x, y), where z = x + iy is a complex number, u(x, y) is the real part of the function, and v(x, y) is the imaginary part of the function.
| 2. How are complex functions different from real functions? | |
Ans. Complex functions differ from real functions as they operate on complex numbers instead of real numbers. While real functions map real numbers to real numbers, complex functions map complex numbers to complex numbers. Complex functions can exhibit more complex behavior, such as rotational or spiraling patterns, which are not possible with real functions.
| 3. What is the concept of analyticity in complex functions? | |
Ans. Analyticity is a fundamental property of complex functions. A function is said to be analytic in a region if it has a derivative at every point within that region. Analytic functions possess many important properties, such as having a power series representation, being infinitely differentiable, and satisfying the Cauchy-Riemann equations.
| 4. What is the significance of Cauchy-Riemann equations in complex functions? | |
Ans. The Cauchy-Riemann equations play a crucial role in the study of complex functions. These equations provide necessary and sufficient conditions for a complex function to be analytic. They establish a relationship between the partial derivatives of the real and imaginary parts of a complex function, enabling us to determine if a given function is analytic or not.
| 5. How are complex functions used in real-world applications? | |
Ans. Complex functions find applications in various scientific and engineering fields. They are used in electrical engineering to analyze the behavior of alternating current circuits, in fluid dynamics to model the flow of fluids, in signal processing for analyzing complex signals, and in quantum mechanics to describe wavefunctions. Complex functions are also extensively used in complex analysis, a branch of mathematics that studies functions of complex variables.
Related Exams
About this Document
|
4.95/5 Rating |
|
Nov 21, 2024 Last updated |
Document Description: Complex Functions for Civil Engineering (CE) 2024 is part of Topic wise GATE Past Year Papers for Civil Engineering preparation.
The notes and questions for Complex Functions have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Complex Functions covers topics
like and Complex Functions Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Complex Functions.
Introduction of Complex Functions in English is available as part of our Topic wise GATE Past Year Papers for Civil Engineering
for Civil Engineering (CE) & Complex Functions in Hindi for Topic wise GATE Past Year Papers for Civil Engineering course.
Download more important topics related with notes, lectures and mock test series for Civil Engineering (CE)
Exam by signing up for free. Civil Engineering (CE): Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
Description
Full syllabus notes, lecture & questions for Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) - Civil Engineering (CE) | Plus excerises question with solution to help you revise complete syllabus for Topic wise GATE Past Year Papers for Civil Engineering | Best notes, free PDF download
Information about Complex Functions
In this doc you can find the meaning of Complex Functions defined & explained in the simplest way possible. Besides explaining types of
Complex Functions theory, EduRev gives you an ample number of questions to practice Complex Functions tests, examples and also practice Civil Engineering (CE)
tests
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
mock tests for examination
,past year papers
,Free
,Viva Questions
,Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
,Summary
,Important questions
,Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
,practice quizzes
,MCQs
,video lectures
,study material
,Semester Notes
,Complex Functions | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
,Extra Questions
,Objective type Questions
,ppt
,shortcuts and tricks
,Exam
,Sample Paper
,Previous Year Questions with Solutions
;
Additional Information about Complex Functions for Civil Engineering (CE) Preparation
Complex Functions Free PDF Download
The Complex Functions is an invaluable resource that delves deep into the core of the Civil Engineering (CE) exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Complex Functions now and kickstart your journey towards success in the Civil Engineering (CE) exam.
Importance of Complex Functions
The importance of Complex Functions cannot be overstated, especially for Civil Engineering (CE) aspirants.
This document holds the key to success in the Civil Engineering (CE) exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Complex Functions Notes
Complex Functions Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Complex Functions.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Complex Functions Notes on EduRev are your ultimate resource for success.
Complex Functions Civil Engineering (CE) Questions
The "Complex Functions Civil Engineering (CE) Questions" guide is a valuable resource for all aspiring students preparing for the
Civil Engineering (CE) exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Complex Functions on the App
Students of Civil Engineering (CE) can study Complex Functions alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Complex Functions,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Complex Functions is prepared as per the latest Civil Engineering (CE) syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup