MTH632 quiz #1 SOLUTION
Complex Analysis And Analytical Geometry
Module# 029 to 050 (Lecture# 01 to 20)
Quiz No#01
Multiple Choice Questions With Correct Answers.
1. The derivative of f at z0 i.e. 𝑓 ′ (z)= limz→z0 f z −f(z0) z−z0 provided the limit exists. The function must be defined is a neighborhood of ____
Correct
Answer is:-z0
2.
If a function f z = u (x, y )+ iv(x, y) is
analytic in a domain D, then its component functions u and v are _____ in D.
Correct
Answer is:-Harmonic
3.
If
Cauchy – Riemann equations are not satisfied at a point z0 then function is not
________ at z0 .
Correct
Answer is:-Differentiable
4.
If f z = x + ay + i(bx + cy) is analytic, then
a, b, c equals to______.
Correct Answer is:-c=1 and a=-b
5 In the complex valued function z=x-iy, the
value of Ux=_____________
Correct
Answer is:-1
6. In the complex valued function z=x-iy, the
value of Vx=_____________
Correct
Answer is:- 0
7.
In the complex valued function z=x+iy, the
value of Ux=_____________
Correct Answer is:-1
8.
In
the complex valued function z=x+iy, the value of Vx= __________
Correct Answer is:-0
9.
Consider
limz→z0 f(z) = A and limz→z0 g(z) = B then the limz→z0 (f(z) ± g (z) ) = ________
Correct Answer is:-A ± B
10.
Consider
limz→z0 f(z) = A and limz→z0 g(z) = B then the limz→z1 (f (z) g( z) ) =
________
Correct Answer is:-A.B
11.
If
Cauchy – Riemann on a pair of real – valued functions of two real variables
u(x,y) and v(x,y) are Ux=Vy and ___.
Correct Answer is:-Uy= -Vx
12 .
A
function f(z) is analytic function if ______________ part of f(z) is analytic.
C.
Correct Answer is:-Both (a) and (b)
13.
Harmonic conjugate of u(x,y)=eycos
x is __________.
Correct Answer is:-ey Sin x+ C
14.
The
sequence zn = 1 n 3 n = 1,2,3,4, … … for n → ∞ converges to ________.
Correct Answer is:-0
15.
Any polynomial p z = a0 + a1z + a2z 2 + ⋯ … … . . + anz n (an ≠ 0) of degree n n ≥ 1 has least one zero,
i.e. there exists at least ------------- Z0 such that P Z0 = 0
Correct Answer is:-One point
16.
Each
simple closed curve C divides the plane into two domains (Connected Open Sets).
One of which is unbounded and is called the ______ of C.
Correct Answer is:-Exterior
17.
A
curve C is said to be a contour if it is constructed by joining finitely many
smooth curves end to end
Correct Answer is:-True
18.
A
function V is said to be harmonic if and only if ___________________
Correct Answer is:-Vxx+Vyy=0
19.
The
sequence zn = −3 + i 1 n 3 n = 1,2,3,4, … … converges to ______________-
Correct Answer is:--3
20.
Each
simple closed curve C divides the plane into two domains (Connected Open Sets).
One of which is bounded and is called the ___ of C.
Correct Answer is:-Interior
21.
If eaxcos y is harmonic then ‘a’ is _____________.
Correct Answer is:--1
22.
A
domain D (Connected Open Set) is called ____________ connected if interior of
every simple closed contour C is contained in D.
Correct Answer is:-Simply
23. If we write ∆𝑧= 𝑧 − 𝑧0 ,𝑡h𝑒𝑛 𝑡h𝑒 𝑓𝑢𝑛𝑐𝑖𝑡𝑜𝑛
can be expressed as 𝑓 ′(𝑧0) = ____
Correct Answer is:-
24.
If U
and V are harmonic functions then f(Z)=U+iV is_________________.
Correct Answer is:-Analytic Function
25. Consider limz→z0 f(z) = A and limz→z0 g(z) = B then the
________
Correct Answer is:-𝐴𝐵 , 𝐵 ≠ 0
26.
A
Cauchy – Riemann equations are satisfied at a point z0 then function _______
differentiable at z0 .
Correct Answer is:-C. Both (a) and (b)
27.
A
point at which a function ceases to be analytic is called a _________ point.
Correct Answer is:-Singular
28.
Cauchy-Riemann
equations are
Correct Answer is:-Ux=Vy and Uy=-Vx
29. If f(z)=u+iv in polar form is analytic then
is
Correct Answer is:- 
30. If f(z)=u+iv in polar form is analytic then
is
Correct Answer is:- 
31 .
A
function v is called a conjugate harmonic function for a harmonic function u in
Ω whenever
Correct Answer is:-f=u+iv is analytic
32.
The
function f(x+iy)=x3 +ax2 y+bxy2 +cy3 is analytic if
Correct Answer is:-a=3i, b= -3 and c=i
33.
There
exist no analytic function f such that
Correct Answer is:-Re f(z)=y2 -2x
34. The harmonic conjugate of
is
Correct Answer is:- 
35.
The
harmonic conjugate of u(x,y)=2x(1-y) is
Correct Answer is:- 
36.
If
the real part of an analytic function f(z) is
, then imaginary part is,
Correct Answer is:-2xy+x
37.
If
the imaginary part of an analytic function f(z) is 2xy+y, then real part is
Correct Answer is:- 
38. 
is differentiable
Correct Answer is:-Nowhere
39. 
is differentiable
Correct Answer is:-Only at z=0
40. 
is
Correct Answer is:-Differentiable at z=0
but not analytic at z=0
41 . 𝑖𝑓
then f(z) is
Correct Answer is:-Not differentiable at
z=0
42. 
is analytic
CCorrect Answer is:-Everywhere
43. 
𝑖𝑠
Correct Answer is:-Not analytic
44.
If
f(z) is analytic then is
Correct Answer is:-Analytic
45.
The
point at which is not analytic are;
Correct Answer is:-i and -i
46.
The
harmonic conjugate of is
Correct Answer is:-
47.
If 𝑓𝑧 = 𝑧(2 −
𝑧) then f(1+i)=
Correct Answer is:- I
48.
If 𝑓𝑧 = then f(3-4i)=
Correct Answer is:- 5
49. If
and g(z)=z+2
then
Correct Answer is:-127
50.
If
and g(z)=z+2
then
Correct Answer is:-66
51. 
then
Correct Answer is:- 1/16
52.
If
then
Correct Answer is:-i
53.
If a function f(z)=u(x,y)+iv(x,y) is analytic
in Domain D, then its component functions u and v are _______________ in D.
Correct Answer is:-Harmonic
2 Comments
Masha Allah, Good Effort, and tabdeeli
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