1 9. Expand f(z) = (2-1)-(2-6) as a Laurent series a) for 12-11 > R. R=?...
in a laurent series valid (z-2) (1+2) 2+11 > 2
Solve:
Laurent series h(z) - Z O CIZ + 11 <3 (2+1)(2-2)
A)
B)
C)
1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
) 1. Find the Laurent series of f(z) on the indicated domain. (a) -,2, on 0 < |z-i| < 2. 1+22 222z 5 , on z 1| > 1
+ for (a)0</zl</ (6) 12/> 1. -6) Find the two Laurent series in powers of z that represent sin --
Q3: 5 marks (A) Expand f(z) (2-1)(2-3) in a Laurent series valid for (i) Iz - 11 < 2, and (ii) Iz - 31 < 2. 1.5 marks each part (B) Use Laurent series to find the residue of f(2)= e (x - 2)-2 at its pole z = 2. 2 marks
Find the different laurent series in the corresponding domains: 1 (2-1) (2-2) ,0< 12-11 <1;1<12-21 <.
[Q3.] Expand f(x) = - via a Laurent series valid for 2 > 1. z(1 - 2)2 va
exercise 4 please
1. Expand the function in a Laurent series that converges for 0 < [z] <R and determine the precise region of convergence. Show details. a. zz-1) (10%) 72-73 (10%) ez b. 2. Determine the location and order of the zeros. a. sin 2 (10%) b. coshºz (10%) 3. Residue integration a. Dedz,c: [2] = a (15%) b. $ 273dz,c: [2] => (15%) 4. Evaluate the following integrals. Show details. a. Lorem (15%) b. Lo**ay (15%)
Let z=5 where x, y, z E R. Prove that z? +z2+z?>