Page 149 - Engineering Mathematics Workbook_Final

Complex Variables

−
 −
f
88. An analytic function ( ) z is such (d) 1,1 2 ,1 2 − 2
=
z
Re
that ( f 1 ( )) 2y and
4
2
2 0
93. The roots of z − z − 2z + = are
f (1 i+ ) 2= then imaginary part of

(a) 1
f ( ) z =
(b) 1 i− 
2
2
(a) 2xy− (b) x − y
(c) both (a) & (b)
2
2
(c) 2xy (d) y − x (d) neither (a) nor (b)
2
f
89. The function ( ) z = z maps first 94. Consider the functions
quadrant onto ___ f ( ) z = x + 2 iy and
2
(a) itself (b) upper half
plane (c) third quadrant (d) right g ( ) z = x + 2 ixy at z = 0
half plane

)
−
90. Let u = 2x (1 y for real x and y (a) f is analytic, but not g
)
v
then a function ( , x y so that
(b) g is analytic but not f
+
f ( ) z = u iv is analytic

2
2
(a) x − 2 ( y − ) 1 (b) ( x − ) 1 + 2 y (c) both f and g are analytic
2
2
(c) ( x − ) 1 − 2 y (d) x + 2 ( y − ) 1 (d) neither f nor g is analytic

− −
91. If z − 1 = 2 , then zz z z = z
95. Lt is
z→ 0 z
(a) 1 (b) 2

(a) 0
(c) 3 (d) 4
(b) 1
2
92. If 1,  ,  are cube roots of units,
3
then the roots of (x − ) 1 + = are (c) 1
8 0
2
(a) 1, 1, 1− − −
(d) does not exists

(b) 1, ,2 

(c) 1 1 2 ,1 2− + +  + 2

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