Jeremy C. Zodinliana posted an Question

August 01, 2021 • 19:59 pm 30 points

10. if f{z) is an analytic function of z and if fz) is continuous at each point within and on a closed contour c, then (a) jfd =0 (6) jf:de =27 f the (c) jfd =2

10. If f{z) is an analytic function of z and if fz) is continuous at each point within and on a closed contour C, then (a) Jfd =0 (6) Jf:de =27 f the (c) Jfd =27i (d) None of the above ) 25 11. The singularity of the function f) = is at (a) z= 1 (b) z = 2 (c)z =4 (d)z= +2 ) 6-i 12. For a cyclic integral f)d, wh 300 (a) radius=2, centre at (1, 0) (b) radius = 1, centre at (1, 0) (c) radius= 2, centre at (0, 1) (d) radius = 1, centre at (0, 1) 13. The value of , where C is a closed curve is (a) 0 if Cencloses the origin (b) 2ti if Cencloses the origin (C) is 2ti if C does not enclose the origin (d) None of the above. 14. The function fz) is analytic at all points within and on C u except at z = Zo Then (a) d =2rif(z,) z- (b) d: =2ri z-0 y O (c) dz = 2ri Jdz (d) 15. The function f(2) = has a (z-z+1)* (a) simple pole at z = 1 &a pole of order 2 at z =-1 (b) simple pole at z -18a pole of order 2 at z =1 (c) simple poles at z = 1 & at z = -1 (d) poles of order 2 at z = 1 and at z=-1 16. The function f(2) = has +a e (a) two simple poles at z = ia and at z = -ia (b) two simple poles atz =a and at z = -a ()a simple pole at z =a and a pole of order 2 at z = -a (d) a simple pole at z = ia and a pole of order 2 at z = -ia 17. If C is the circle defined by |z| > 1, then the value of the integral is *+z (a) 0 (b) 277 (c) 27i d) -2T 18. If Cis the circle of radius r = |z|l = 3/2, then the valu the integral -I(2-2) (a)o (b) 277 (C) 27ti (d)- 2Ti

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