Page 155 - Engineering Mathematics Workbook_Final

Complex Variables
−
− −
1 (a) 1, 1, 1

132. Let ( ) z = for all z C such
f
e − 1 (b) 1, , 2
z
that e  1. Then 
z
− + +
2
+
(a) f is meromorphic (c) 1 1 2 , 1 2
(b) the only singularities of f are (d) 1,1 2 ,1 2− −  − 2
poles.
137. Which of the following is possible
(c) f has infinitely many poles on the value for the imaginary part of
imaginary axis ln ( )
i

(d) Each pole of f is simple.

z − 1 (a)  (b)
133. Let ( ) z =   then, 2
f
exp   2 i      − 1 
 z  (c) (d) 
4 8
(a) f has an isolated singularity at
z = 0 [GATE]

(b) f has a removable singularity at 138. e is a periodic with a period of
z
z=1

(c) f has infinitely many poles (a) 2 (b) 2 i 

(d) each pole of f is of order 1. (c)  (d) i

134. If z − 1 = 2 , then zz − − = ____ [GATE-1997-CE]
z
z
139. Which one of the following is not
135. Given to complex numbers true for complex number z and z ?

5 3 i and z =
z = 5 + ( ) 2 + 2i 1 2
1
2
3 z z z
(a) 1 = 1 2
z z 2
the argument of 1 in degree is 2 z 2
z 2 (b) z + z  z + z
2
1
2
1
(a) 0 (b) 30
(c) z − z  z − z
2
2
1
1
(c) 60 (d) 90
(d) z + z 2 + z − z 2 = 2 z 2 + 2 z 2
136. If 1, ,  2 are cube roots of units, 1 2 1 2 1 2
3
then the roots of (x − ) 1 + 8 0 are [GATE-2005-CE]
=

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