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Complex Analysis
Note: Red color option is the correct answer of the question
...
The upper bound of the function

z 2 +3
z 2 −z−6

, when |z| = 1 is

(A) 2
(B) 1
(C) 2/3
(D) 1/3
2
...
+ cos nα is
(A)

cos(nα/2) sin[(n+1)α/2]
sin(α/2)

(B)

sin(nα/2) sin[(n+1)α/2]
sin(α/2)

(C)

cos(nα/2) sin[(n+1)α/2]
cos(α/2)

(D)

sin(nα/2) cos[(n+1)α/2]
sin(α/2)

√
3
...
If 1, ω, ω 2 ,
...
+ nω n−1
equals
(A)
(B)
(C)
(D)

−n
1−ω
n
1−ω
−n
1+ω
n
1+ω

5
...
Let n I
...
Then Re(z1 z2 ) =
¯
|z1 ||z2 | ⇔
(A) θ1 − θ2 = 0
(B) θ1 − θ2 = 2nπ
(C) θ1 − θ2 = nπ
(D) none of these
7
...
Then we must have
(A) Im(z) = 1/2
(B) Im(z) = −1/2
(C) Re(z) = Im(z)
(D) Im(z) = 0
8
...
32i32 = a + ib, where a and b are real, then order
pair (a, b) is
(A) (16, 1)
(B) (16, −16)
(C) (4, 12)
(D) none of these
√

9
...
The set of points z C for which |z − 2| + |z + 2i| = 4 is the conic
(A) hyperbola
(B) parabola
(C) square
(D) ellipse
11
...
The solution of the equation e2z + ez+1 + ez + e = 0 is
(A) πi
(B) πi + 1
(C) 1 + 3πi
(D) all of the above
13
...
If z1 and z2 are complex number, then z1 z2 + z1 z2 = 0 implies
(A) z1 and z2 are perpendicular
(B) z1 and z2 are parallel
(C) z1 and z2 are at angle

π
3

(D) none of these
15
...
If z1 and z2 are non-zero complex numbers, such that |z1 | = |z2 | and Arg(z1 ) +
Arg(z2 ) = 2π then z1 equals
(A) z2
(B) −z2
(C) z2
(D) −z2
17
...
If z =

√
3i
1
+
2
2

5

+

√
3i
1
−
2
2

5

, then

(A) Re(z) = 0
(B) Im(z) = 0
(C) Re(z) > 0 Im(z) > 0
(D) Re(z) > 0 Im(z) < 0
19
...
If z1 , z2 and z3 are three distinct complex number and a, b and c are three posb
c
a
=
=
, then the value of
itive real number such that
|z2 − z3 |
|z3 − z1 |
|z1 − z2 |
a2
b2
c2
+
+
is
z2 − z3 z3 − z1 z1 − z2
(A) 0
(B) 1
(C) -1
(D) none of these
21
...
Define bk =
Then 4 bk ω k is equal to
k=0
(A) 5
(B) 5 ω
(C) 5(1+ω)
(D) 0

4
j=0

jω −jk for 0 ≤ k ≤ 4

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