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Question one (9 marks total, 3 marks each) Let f(2)= Z 22-32+2 a. Find a Maclaurin...
) 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
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
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
question 5c 5. Find the Laurent series expansion of: (a) f(x) = 2*1 about i, (b) f(x) = 22 + 1-2, convergent on {2 < 121 <4}, (c)* f(x) = 2,2-33+2, convergent on {j < lz - 11 < 1}.
2 7. Find the Laurent series of the function f(2) = in the region 1 < 121 < 2. (z+1)(2 – 2)
Develop f(z)=1/(z(z-3)) in a laurent series valid for the indicated domains. determine the nature of the singularities of the following functions. 0시리 <3 6) 3<시리 22 13) f(3) = -1 14) FCZ) = sen (42) - 42 Z 22
Complex Analysis: = Define the function 22 f(z) 22 +1 For each annulus region given below, find the Laurent series of f(z) convergent in the region. (a) 0 < 12 – il < 2 (b) 1 < 121.
Question 9 < Textbook 2 Videos [+] Find the Maclaurin series of Per- n=0 Submit Question Jump to Answer
Solve: Laurent series h(z) - Z O CIZ + 11 <3 (2+1)(2-2)
complex anaylsis f(2)= 22 2z 2²+1 For each annulus region below, find the Laurent series of fiz) convergent convergent in the region (i) OC/Z-il<2 12IZI