Do only 1st question..... (1) Show that the function f(2)=2[z], where z=x+3y, is not analytic anywhere in thecomplex plane.(2) It is given that d=42-3 and f(z=1+3)=-33. Find f(z) from the above informationand the harmonic functions u(x, y) and v(x, y) such that f(2)= u(x, y) + (x,y).

1. The given function is fz=zz, where z=x+jy We have to show that fz is not analytic anywhere in the…

Answered: (1) Show that the function f(2)=z|z],…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 25E

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Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii a1=0.1 11. Consider the function f(x)=4x2(1x) a. Find any equilibrium points where f(x)=x. b. Determine the derivative at each of the equilibrium points found in part a. c. What does the theorem on the Stability of Equilibrium points tell us about each of the equilibrium points found in part a? d. Find the next four iterations of the function for the following starting values. i. a1=0.4. ii. a2=0.7 e. Describe the behavior of successive iteration found in part d. f. Discuss how the behavior found in part d relates to the results from part c.
Verify that the function u(x,y)=y^3-3x*2y is harmonic.Find v(x,y), the harmonic conjugate function of u(x,y).Form the corresponding analytic function f(z)= u+iv
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(1) Show that the function f(2)=z|z], where z=z+jy, is not analytic anywhere in the complex plane.