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(5) Use Cauchy Integral Formula to calculateh(2+(i+1), ee is whose vertices are 0, 4, 2- 2i, and -2i. oriented counterclockwise. Assume a suitable branch of (z +4i) c (2+ I)2 + i dz where C is the paralle 5)
Q3: Evaluate (30 points) i cos? (4 + 2i) What is the principle value of the logarithm (40 points) In(-13 - i)
evaluate Σ(1) k=1 n (-1)* k+1 Σ(1). A=0
Exercises aw the contours γ-[0, i], σ [0, l] + [1,1]. Evaluate re z dz re z dz Exercises aw the contours γ-[0, i], σ [0, l] + [1,1]. Evaluate re z dz re z dz
Evaluate the integral $ 3z + 4)cos z dz, C:12+2i = 1 counterclockwise. z² +4 Integrate $c +436 yosz dz, C:/z+3–2i = 3 counterclockwise. (z +4)
(1 point) If A = | -1 0 1+i į 1-2 – 1 0 -1 + 2i] 4 , then –4 + 2i] A-1 =
for x<4 Evaluate m(-3) where m(x) = {22.4 for 45x< 1 |vx-1 for x 21 0-13 O 2, 5, 2i O2 O 2.5 O 5
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a Ct - ;) e ① & 2 + 1 - ② i + ti
Let A = [2-3i 3 + 2i [ 5 - 1+i –1 + i 21 1-11 -1-il -2 ] The set of solutions to the equation Ax = 0 is 22 = [Select] 23+ [Select] 21
| 1. Let z = 1+ 2i z = -2-2i, z = 3, 24 =i A. Complex arithmetic (20%) | a. Zi + Z2 b. Z1Zz sle Isles B. Determine the principle value of the argument and graph it (20%) a. 21 b. Z2 c. 23 d. 24