>
Exams
>
Mathematics
>
Analytic functions
>
if u x 2 y 2 is real part of an analytic function
Question:
If
\(u = x^2 - y^2\)
is real part of an analytic function f(z), then f(z) is:
CUET (PG) - 2023
CUET (PG)
Updated On:
Mar 12, 2025
Z
Z
2
\(\bar Z^2\)
\(Z+\frac{1}{Z}\)
Hide Solution
Verified By Collegedunia
The Correct Option is
B
Solution and Explanation
The correct option is(B)
Download Solution in PDF
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 ME - 2024
Engineering Mathematics
Analytic functions
View Solution
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
View Solution
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
View Solution
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
View Solution
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 Solution
View More Questions
Questions Asked in CUET PG exam
What are the primary components of a lipid raft in the context of bio-nanoelectronics?
CUET (PG) - 2026
Nanoelectronics Applications in Industry
View Solution
Which property refers to the inability to repeat recorded data when scanning from different directions?
CUET (PG) - 2026
Electronic devices
View Solution
In optical fibers, does the core or the cladding have a higher refractive index?
CUET (PG) - 2026
Electronics
View Solution
What is the word length of a standard 8085 microprocessor?
CUET (PG) - 2026
Electronic devices
View Solution
Which scientist is widely regarded as the Father of Nanotechnology?
CUET (PG) - 2026
Nano-technology and Applications
View Solution
View More Questions