Page 153 - Engineering Mathematics Workbook_Final

Complex Variables

z
f
120. Let ( ) z = . Then z + 2 2z − 1
(a) C  z − 2 dz = 2 i  , where C
( )
(a) lim f z does not exist is a circle z = 3
z→ 0
(b) f is continuous at z = 0 z + 2 2z − 1
(b) C  dz = 14 i  , where
(c) f is not differentiable at z = 0 z − 2
(d) f is not regular at z = 0 C is a circle z = 3

2
121. Let ( ) z = z . Then z + 2 2z − 1
f
(c) C  2 dz = 12 i  , where
(a) Cauchy-Riemann equations are (z − ) 2
satisfied only at z = 0 C is a circle z = 3

(b) Cauchy-Riemann equations are (d) C  z + 2 2z − 1 dz = 4 i  , where C
satisfied for all z (z − ) 2 2

(c) Cauchy-Riemann equations are is a circle z = 3
not satisfied at any values of z

124. Let ( ) z = cos (z − ) 1 , then
f
(d) f is not analytic at z = 0 z − 1
122. Consider the function (a) f(z) has simple pole at z = 1

 e − z − 4 , if z  0 (b) f(z) has isolated essential

f ( ) z =  . Then singularity at z = 1
 0, if z = 0


which of the following (s) is / are (c) residue of at z = 1 is undefined
correct? (d) residue of f at z = 1 is 1

(a) Cauchy-Riemann equations are ze z
f
not satisfied at z = 0 125. Let ( ) z = z − 1 . Then

(b) Cauchy-Riemann equations are C  1
0
satisfied at z = 0 (a) f ( ) z dz = on :C z = 2

(c) f is not analytic at z = 0 1
(b) f(z) is analytic on z =
(d) f is analytic at z = 0 2
1
123. Which of the following (s) is correct? (c) f(z) is analytic within z 
2
1

(d) f(z) is not analytic outside z 
2

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