Question:
If \(u = x^2 - y^2\) is real part of an analytic function f(z), then f(z) is:
If \(u = x^2 - y^2\) is real part of an analytic function f(z), then f(z) is:
Updated On: Mar 12, 2025
- Z
- Z2
- \(\bar Z^2\)
- \(Z+\frac{1}{Z}\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is(B)
Was this answer helpful?
0
1
Top Questions on Analytic functions
- Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is
- GATE Metallurgy - 2024
- Engineering Mathematics
- Analytic functions
- Match List I with List II
LIST I LIST II A. \(f(z)=z^3\) I. Not analytic any where B. \(f(z)=\frac{1}{z}\) II. Analytic at Z = 0 only C. \(f(z)=\bar z\) III. Analytic everywhere D. \(f(z)=z\bar z\) IV. Not analytic at Z = 0 Choose the correct answer from the options given below:- CUET (PG) - 2023
- Mathematics
- Analytic functions
- If\(ƒ(x + iy) = x^3 − 3.xy^2 + ¡\Psi(x,y) \space where \space i= \sqrt{-1}\) and ƒ (x+iy) is an analytic function, then \(\Psi (x, y)\) is:
- CUET (PG) - 2023
- Mathematics
- Analytic functions
- Given below are two statements
Statement I: If f(z) = u + iv is an analytic function, then u and v are both harmonic function.
Statement II: If f (z) is analytic within and on a closed curve C, and if a is any point within C, then \(f(a)=\frac{1}{2πi}\int_c\frac{f(z)}{z-a}dz\)
In the light of the above statements, choose the most appropriate answer from the options given below- CUET (PG) - 2023
- Mathematics
- Analytic functions
- Given $z = x + iy$, $i = \sqrt{-1}$. $C$ is a circle of radius $2$ centred at the origin and traversed anticlockwise. The value of \[ \frac{1}{2\pi i} \int_C \frac{1}{(z-i)(z+4i)}\, dz \] is ____________ (round off to one decimal place).
- GATE ME - 2022
- Engineering Mathematics
- Analytic functions
View More Questions
Questions Asked in CUET PG exam
- Arrange the following in an organization's human resource management process in the correct order:
- CUET (PG) - 2025
- Human Resource Management
- Which of these books are not written by Munshi Premchand?
(A) Gora
(B) Gaban
(C) Chitra
(D) Mahabhoj
Choose the correct answer from the options given below:- CUET (PG) - 2025
- General Awareness
- The given sentence is split into segments and one of the segments may have an error. Identify the segment with an error from the options given below: (A) The declining birth rate in developed (B) nations is being interpreted as an response to (C) the rising cost of living and inadequate care-giving structures.
- CUET (PG) - 2025
- English Usage Errors
- Which of the following is a Christian majority state in India?
- CUET (PG) - 2025
- Geography
- Who among the following were known as the University Wits?
(A). John Lyly
(B). Ben Jonson
(C). Thomas Nashe
(D). Thomas Middleton
Choose the correct answer from the options given below:- CUET (PG) - 2025
- English Literature
View More Questions