Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(iii) af A function is analytic if = 0. Prove that f(x, y) = az x-1-ty (x-1)²+y² is analytic.

(iii) af A function is analytic if = 0. Prove that f(x, y) = az x-1-ty (x-1)²+y² is analytic.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
See similar textbooks
icon
Related questions
Question
Document Took Window Help 1 143% Find (iii) A function is analytic if af = 0. Prove that f(x, y) = X-1-ty (х-1)2+ у? is analytic. %3D az Q#3:- Solve the following: (i) Construct the analytic function f(z) in term of 'z' whose imaginary part is V(x, y) = -(y³ + 6xy – 3x²y – 3y). Show that U(x, y) is Harmonic function. (ii) Verify that U(r, 0)and V(r, 0) of f(z) = In(x² + y²) + 2t tan-1 (2) both are Harmonic in Polar form. (iii) If f(z) = z², z # 0. Find the level curves U = cq and V = c2 and verify the orthogonality of these curves.
Transcribed Image Text:Document Took Window Help 1 143% Find (iii) A function is analytic if af = 0. Prove that f(x, y) = X-1-ty (х-1)2+ у? is analytic. %3D az Q#3:- Solve the following: (i) Construct the analytic function f(z) in term of 'z' whose imaginary part is V(x, y) = -(y³ + 6xy – 3x²y – 3y). Show that U(x, y) is Harmonic function. (ii) Verify that U(r, 0)and V(r, 0) of f(z) = In(x² + y²) + 2t tan-1 (2) both are Harmonic in Polar form. (iii) If f(z) = z², z # 0. Find the level curves U = cq and V = c2 and verify the orthogonality of these curves.
-2i (ii) Compute zez dz z2 +1 Where C: z| = 2 is the circle of radius 2 center a O oriented counterclockwise. (iii) Evaluate f edz, from z = 1 to z = 1+talong the line x = 1.
Transcribed Image Text:-2i (ii) Compute zez dz z2 +1 Where C: z| = 2 is the circle of radius 2 center a O oriented counterclockwise. (iii) Evaluate f edz, from z = 1 to z = 1+talong the line x = 1.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
SEE MORE TEXTBOOKS