Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Questions  >  If f (z) is an analytic function whose modulu... Start Learning for Free
If f (z) is an analytic function whose modulus is constant, then f (z) is a
  • a)
    Function of z
  • b)
    Constant
  • c)
    Function whose only imaginary part is constant
  • d)
    Function whose only real part is constant
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If f (z) is an analytic function whose modulus is constant, then f (z)...
Concept:
Let f(z) = u + iv be the analytic function,
then According to Cauchy-Riemann Equations
ux = vy & uy = - vx
Calculation:
Given:
modulus is constant
= k ⇒ u2 + v2 = k
Now differentiating both sides w.r.t x and y, we get
2uux + 2vvx = 0 ⇒ 2uux = -2vvx      --- (1)
2uuy + 2vvy = 0 ⇒  2uuy = -2vvy     --- (2)
Now applying Cauchy-Riemann Equations ux = vy & uy = - vx
2uux – 2vuy = 0 ⇒ 2uux = 2vuy     --- (3)
2uuy + 2vux = 0 ⇒ 2uuy = -2vux     --- (4)
Now dividing equations 3 and 4, we get 

⇒ ux = uy = 0 ⇒ u is a constant function.
Similarly, we will get v is a constant function.
∴ f(z) is a constant function.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer?
Question Description
If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer?.
Solutions for If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If f (z) is an analytic function whose modulus is constant, then f (z) is aa)Function of zb)Constantc)Function whose only imaginary part is constantd)Function whose only real part is constantCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

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