>
Exams
>
Mathematics
>
Analytic functions
>
if x iy x 3 3 xy 2 x y where i 1 and x iy is an an
Question:
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
CUET (PG)
Updated On:
Mar 21, 2024
\(y^3-3x^2y\)
\(3x^2y-y^3 \)
\(x^4-4x^3y \)
\(xy-y^2\)
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
0
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
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
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
\(u = x^2 - y^2\)
is real part of an analytic function f(z), then f(z) is:
CUET (PG) - 2023
Mathematics
Analytic functions
View Solution
View All
Questions Asked in CUET PG exam
Find out the degree of the differential equation
\(\frac {d^2t}{ds^2}+(\frac {dt}{ds})^2+2t=0\)
CUET (PG) - 2023
Differential Equations
View Solution
The surface area of the sphere x
2
+ y
2
+ z
2
= 9 lying inside the cylinder x
2
+ y
2
= 3y is
CUET (PG) - 2023
Surface Area of Cube, Cuboid and Cylinder
View Solution
The Ombudsman in a newspaper organisation represents the point of view of the ___.
CUET (PG) - 2023
Journalism
View Solution
The orthogonal trajectories of the family of curves y =
\(ax^3\)
is
CUET (PG) - 2023
Curves
View Solution
The minimum distance of the point (3, 4, 12) from the sphere x
2
+ y
2
+ z
2
= 1 is
CUET (PG) - 2023
Coordinate Geometry
View Solution
View More Questions