Page 138 - Engineering Mathematics Workbook_Final

Complex Variables

8. The value of the integral 12. The fixed points of ( ) z = 2iz + 5
f


2
 sin z + cos z 2 dz where C is z − 2i
C (z − 4 )(z − ) 2 are
the circle z = 3 traced anti- (a) 1 i (b) 1 2i


clockwise, is
(c) 2i  1 (d) i  1
−
(a) 2 i  (b) i 
2
f
13. The function ( ) z = z is
−
(c) i  (d) 2i 
(a) differentiable everywhere
z − sin z
f
9. For the function ( ) z = , (b) differentiable only at the origin
z 3
the point z = 0 is (c) not differentiable anywhere

(a) a pole of order 3 (d) differentiable on real x – axis

(b) a pole of order 2 14. The function ( ) z = z maps the
2
f
(c) an essential singularity first quadrant onto

(d) a removable singularity (a) itself

−
1 e − z (b) upper half plane
f
10. For the function ( ) z = , the
z (c) third quadrant
point z = 0 is
(d) right half plane
(a) an essential singularity
15. The radius of convergence of the
(b) a pole of order zero power series of the function

(c) a pole of order one f ( ) z = 1 about z = 1 is
−
(d) a removable 1 z 4
singularity 1
(a) 1 (b) 4

11. The value of the integral  dz ,
C z − 1 3
2
4
C : z = is equal to (c) (d) 0
4
(a) i  (b) 0

(c) − i (d) 2 i

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