Page 157 - Engineering Mathematics Workbook_Final

Complex Variables

148. All the values of the multi-valued GRAPH OF COMPLEX FUNCTION
complex function 1 , where i = − 1, 2
i
f
are 152. The function ( ) z = z maps first
(a) purely imaginary quadrant onto _____
(b) real and non-negative
(a) itself
(c) on the unit circle (b) upper half plane
(d) equal in real and imaginary parts

[GATE-2014 – EE-SET 2] (c) third quadrant
(d) right half plane
149. Given two complex number

5 3 i and z =
z = 5 + ( ) 2 + 2i, 153. The bilinear transformation
2
1
3 z − 1
z w = z + 1
the argument of 1 in degree is
z
2
(a) maps the inside of the unit circle
(a) 0 (b) 30 in the z-plane to the left half of the w-
(c) 60 (d) 90 plane
[GATE-2015-ME-SET 1]
(b) maps the outside the unit circle in
150. Which one of the following options
correctly describes the location of the the z-plane to the left half of the w-
4
2
roots of the equation s + s + = plane
1 0
on the complex plane? (c) maps the inside of the unit circle
(a) Four left half plane (LHP) roots in the z-plane to right half of the w-

(b) One right half plane (RHP) root, plane
one LHP root and two roots on the
imaginary axis (d) maps the outside the unit circle in
the z-plane to the right half of the w-
(c) Two RHP roots and two LHP plane
roots

[GATE-2002 (IN)]
(d) All four roots are on the
imaginary axis 154. For the function of a complex
variable W = ln Z (where, W = u + jv
[GATE-2017 EC SESSION-1]
and

151. Let z = x + jy where j = − 1 . Z = x + jy), then u = constant lines

Then cos z = get mapped in z-plane as

(a) set of radial straight lines
(a) cos z (b) cos z
(b) set of concentric circles
(c) sin z (d) sin z

[GATE-2017 (IN)]

155