Page 160 - Engineering Mathematics Workbook_Final

Complex Variables

for which the function f(z) is analytic (c) 2x + x +
−
is ______. x + y 2 C
2
[GATE-2016-EC-SET 2] y
(d) 2xy − + C
2
162. What is value of the m for which x + y 2
2x x + 2 my is harmonic?
2
−
[ESE 2017 (COMMON PAPER)]
(a) 1 (b) -1
165. The value of  zdz from z = 0 to z =

(c) 2 (d) -2 c
4 + 2i along the curve ‘c’ given by
=
[ESE 2017 (EE)] z t + 2 it
CONSTRUCTION OF AN ANALYTIC 8i 8
FUNCTION (a) 10 − (b) 10i +
3 3

163. The real part of an analytic function 8
f(z) where z = x + jy is given by (c) 10 − (d) 0
3i
e − y cos ( ) x . The imaginary part of
166. If z is a complex variable, the value
f(z) is 3i
of  dz
−
(a) e y cos ( ) x (b) e y sin ( ) x 5 z

(c) e − y sin ( ) x (d) e − − y sin ( ) x (a) -0.511 – 1.57i

(b) – 0.511 + 1.57i
[GATE-2014-EC-SET 2]
(c) 0.511 – 1.57i
164. If W  = i + represents the
complex potential for an electric (d) 0.511 + 1.57i
field.
[GATE-2014-ME-SET 1]
x
2
2
Given  = x − y + , then
x + y 2 167. Consider the line integral
2
)
2
the function  is I = (  x + 2 iy dz , where z = x +
c
y iy. The line c is shown in the figure
(a) 2x− + + C below.
2
x + y 2
x
(b) 2xy + + C
2
x + y 2

158