Question

plz help me solve the question.

plz dont copy anyother wrong answer.

Ouestion 2. 2/2 -Throughout this question, z E C \ R and we define do (a) Locate and classify all singularities in the complex plane of Determine any associated residues (b) Evaluate Φ(z) by completing the contour in the upper half-plane. (c) Evaluate Ф(z) by completing the contour in the lower half-plane. (d) Verify that your answers to (b) and (c) are the same. (e) If r e R and y e R\ f0), use results you have obtained earlier in answering this question to show that lim. Φ(x + iy)- lin . Φ(z + i)-1+z? (f) If x R, use a contour integral technique to evaluate the Cauchy principal value integral Locate and classify all singularities in the complex

Answer 1

0 2. Defime 2 ore simple pole All these siwanities arim

Res(as)) = Linn s-1) 计)(1-2) andRes (als)-) γη 2i i-2) Res (Q(4)?) and 2) tim (5- .eiXsti)G-う

has only one 시ng ulanity a+Koci 2i (i2) e In Low er thenand a o singulari ties a(G) 2t (2-i) (2+1) 2i (2-i)(Ftǐ) 2 (2-i 21L 2; (2-1). ame na war i (+2)

lane . Retl pant 2 2: (i-2) la am me 2 e Upper halt plana 2 Upper hall blane. 下/K