Page 151 - Engineering Mathematics Workbook_Final

Complex Variables

105. The value of ‘P’ such that the 109. The value of
function z  cos z dz is

1 1  px   1 = ( z z − 2 )(z − ) 4
2
f ( ) z = log ( x + y 2 ) i+ tan −  
2   y   i  i 
is analytic is (a) (b) −
4 4

(a) 1 (b) -1 (c) i  (d) 2 i 

(c) 2 (d) -2 110. Let ‘C’ be the circle z = 1 in the

sin (z − ) 1 complex plane described in counter
106. The function ( ) z = at z 1 z
+
f
z − 1 clock wise then c  dz
)
−
= 1 is (2 zi z
−
i
(a) removable singular (a) i  (b) 
−
(c) 2 i  (d) 2 i 
(b) essential singular

2

(c) pole of order 2 111. The value of c  sin z + cos z 2 dz
(z − 4 )(z − ) 2
(d) none
where z = 3 is
z − sin z
107. The function ( ) z = at z = (a) 2 i  (b) 2 i 
−
f
z 3
−
i
0 is (c) i  (d) 
(a) removable singular 112. The value of c  sec z dz where ‘C’ is
z = 1 is
(b) essential singular
(a) 0 (b) 2 i 
(c) pole of order 2

(d) none (c) i (d)
2
 1 
108. The function ( ) sinf z =       at c  1
−
 1 z  113. The value of z + 4 dz where ‘c’
2
z = 1 is is

(a) removable singular i 
(a) (b) −
(b) essential singular 2 2
i i
(c) zero of the function (c) − (d)
2 2
(d) none

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