Question

Suppose f(2)= [(2+1)(2+1>] + [cose)} a] Find all the singularities of f(z) and classify each one as either a removable singu

complex anaylsis
please cite any theorems used

0 0
Add a comment Improve this question Transcribed image text
Answer #1

First we find the singularities and then we classify them according to their nature. We use simple limit calculation to find the answer.

For second part it will be hard to find the exact integral value directly, we just use Cauchy Redidue theorem and also use a formula to find residues at a pole.T2 DO (1) Zo SI (20+1)/2, nez _7/2 f(z)= h (z)+ g(2) Where h(z) = (2+1)2 (22-1) upon which DERE ) woowww702)=ON 2. is a singu72 Czeit :)2 (aeftir) * doczerty 7zeit dt -1/2 value upon calculation we may get a definite integral integral wy which is theTVO value carefur) * coppelt) ] zelt dt upon calculation we a definite integraal which is the value of the contour integral!Res (f; 2) lim (2+1) f(2) 27-1 zti CO 2 ling Lan (2-1) tij? (21) woy 96 Res (to 2a) = lim Z+09+) T12 z - Qn+)2] F2) Ain (2011

Add a comment
Know the answer?
Add Answer to:
complex anaylsis please cite any theorems used Suppose f(2)= [(2+1)(2+1>]" + [cose)} a] Find all the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • complex anaylsis (cite all theorems used please) suppose fc z)= [(2+1)²( 2² +1)] + [COS(2)] a]...

    complex anaylsis (cite all theorems used please) suppose fc z)= [(2+1)²( 2² +1)] + [COS(2)] a] Find all the singularities of f(z) and classify each a removable singularity, a pole of order in (and find m), or an essential singularity. one as either

  • complex anaylsis (cite all theorems used) single function at all (if) Find a f(2) which has...

    complex anaylsis (cite all theorems used) single function at all (if) Find a f(2) which has all of the following: - f(z) is discontinuous at the origing and discontinuous at all points z with Arg (Z) = I but fiz) is continuous other points of c. -, and at =1, f has a simple zero at z=i f has pole of order 3 at Z=T (ii) Determine whether (*) below is true or false. If true prove it; it false,...

  • complex anaylsis, cite any theorems used, thanks Z with at (i() Find a single function f(2)...

    complex anaylsis, cite any theorems used, thanks Z with at (i() Find a single function f(2) which has all of the following: - f(z) is discontinuous at the origin and discontinuous at all points Arg (Z) = t but fczy is continuous all other points of c. f has a simple zero at z=í f has a pole of order 3 at Z=T (ii) Determine whether (*) below is true or false. If true prove it it false, give a...

  • Complex Analysis: 1 + COS Z Define the function 1 f(2)= (z + 1)2(23 +1) (a)...

    Complex Analysis: 1 + COS Z Define the function 1 f(2)= (z + 1)2(23 +1) (a) Find all the singularities of f(z) and classify each one as either a removable singulatiry, a pole of order m (and find m), or an essential singularity. (b) Let I = 71+72, where yi and 72 are the directed smooth curves parameterized by TT zi(t) = 2i(1 – 2t), 0 < t < 1 z2(t) = 2eit, 277 < t < 2' respectively. Compute...

  • 1 1 + COS Z 8. Define the function f(x) = (2 + 1)2( 23 +1)...

    1 1 + COS Z 8. Define the function f(x) = (2 + 1)2( 23 +1) (a) (6 points) Find all the singularities of f(z) and classify each one as either a removable singulatiry, a pole of order m (and find m), or an essential singularity. (b) (6 points) Let I = 71+72, where 71 and 42 are the directed smooth curves parameterized by -TT TT zi(t) = 2i(1 – 2t), 05t51 z2(t) = 2eit, sts 2' respectively. Compute Sr...

  • complex anaylsis Only need help on (ii) and (iii), please answer both and cite theorems used...

    complex anaylsis Only need help on (ii) and (iii), please answer both and cite theorems used a one Consider the real valued function ulx,y). with x and y are real variables For Cach definition of ulx,y) below, find whether there Cette exists real-valued function v(x,y) such that f(2)= u(x,y) ti vex,y) is a function analytic in some DEC. If such such v(x,y) and determine the domain analyticity o for fcz). It such a not exist, prove that it does not...

  • Complex anaylsis, cite all theorems used. Y are one Consider the real valued function ulx,y) with...

    Complex anaylsis, cite all theorems used. Y are one Consider the real valued function ulx,y) with x and real variables. For each definition of ucxy) below, find whether there cette exists real-valued function v(x,y) such that f(2)= u(x, y) tivcx,y) is a function analytic in some DEC. If such such v(x,y) and determine V(X,Y) the domain of analyticity D for fcz). It such a not exist, prove that it does not exist. (i) u (x,y)= xy2-x²y (ii) ucx, y) =...

  • 1 - 22) sin(Tz) Consider fe)() a. Find all isolated singularities of f in C and...

    1 - 22) sin(Tz) Consider fe)() a. Find all isolated singularities of f in C and classify each as removable, a pole (specity the order), or essential. b. Explain, with reference to part (a), why f has a series expansion of the form Σ000 ch3k valid near 0. c. Find co d. What is the radius of convergence of the series in part (b)?

  • Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed...

    Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...

  • Complex Analysis: . (a) Find a single function f(z) which has all of the following properties:...

    Complex Analysis: . (a) Find a single function f(z) which has all of the following properties: f(z) is discontinuous at the origin z = 0, at z = 1, and at all points z with Arg(z) = 7/4, but f(z) is continuous at all other points of C; • f(z) has a simple zero at z = :i; and f(z) has a pole of order 3 at z = n. Justify that your function f(x) has each of the properties...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT