Civil Engineering (CE) Exam  >  Civil Engineering (CE) Questions  >  A function f of the complex variable z = x + ... Start Learning for Free
A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____
    Correct answer is between '-1.1,-0.9'. Can you explain this answer?
    Most Upvoted Answer
    A function f of the complex variable z = x + i y, is given as f(x, y) ...
    To find the function f(z), we need to find the expressions for both u(x, y) and v(x, y).

    Given that u(x, y) = 2kxy, we can find the expression for u(x, y) in terms of z:

    u(x, y) = 2kxy = 2k(x)(iy) = 2kxiy

    Similarly, given that v(x, y) = x^2, we can find the expression for v(x, y) in terms of z:

    v(x, y) = x^2 = (x)(x) = (x)(-i)(-i) = (x)(-iy)(-iy) = (-ix)(-iy) = -ixy

    Therefore, the function f(z) is given by:

    f(z) = u(x, y) + iv(x, y) = 2kxiy - ixy = (2kx - i)x(iy - 1)

    So, the function f(z) is f(z) = (2kx - i)x(iy - 1).
    Free Test
    Community Answer
    A function f of the complex variable z = x + i y, is given as f(x, y) ...
    Given u = 2kxy & V = x2 – y2
    Concept:
    For function to be analytic:

    ∴ Apply any of the above condition to get the answer.
    By first condition:
    2ky = -2y ⇒ k = -1
    Explore Courses for Civil Engineering (CE) exam

    Top Courses for Civil Engineering (CE)

    A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer?
    Question Description
    A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer?.
    Solutions for A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE). Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
    Here you can find the meaning of A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer?, a detailed solution for A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? has been provided alongside types of A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A function f of the complex variable z = x + i y, is given as f(x, y) = u(x, y) + i v(x, y), where u(x, y) = 2kxy and v(x, y) = x2 – y2. The value of k, for which the function is analytic is _____Correct answer is between '-1.1,-0.9'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
    Explore Courses for Civil Engineering (CE) exam

    Top Courses for Civil Engineering (CE)

    Explore Courses
    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev