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JEE Questions for Maths Complex Numbers Quiz 3 - MCQExams.com
JEE
Maths
Complex Numbers
Quiz 3
The value of (1+ √3i )
4
+ (1 - √3i)
4
is
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0%
-16
0%
16
0%
14
0%
-14
If the fourth roots of unity are z
1
, z
2
, z
3
and z
4
, then z
2
1
+ z
2
2
+ z
2
3
+ z
2
4
is equal to
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0%
0
0%
2
0%
3
0%
None of these
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(- 3,
0%
(0, 3)
0%
(0, -
0%
If ω # 1 is a cube root of unity, then the sum of the series S = 1+ 2ω+ 3ω
2
+ • • • + 3ω
3n-1
is
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0%
0%
3n(ω - 1)
0%
0%
0
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cos nθ - i sin nθ
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cos nθ + i sin nθ
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cos 2nθ - i sin 2nθ
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cos 2nθ + i sin 2nθ
If z = cos θ + i sin θ, then the value of
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0%
0%
2)
0%
0%
If a is a complex number satisfying the equation α
2
+ α + 1= 0, then α
31
is equal to
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0%
α
0%
α2
0%
1
0%
i
The smallest positive integral value of n such that
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0%
4
0%
3
0%
2
0%
8
If n is a positive integer, then (1+ i√3)
n
+ (1 - i√3)
n
is equal to
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0%
2n-1 cos nπ/3
0%
2n cos nπ/3
0%
2n+1 cos nπ/3
0%
None of these
If n is an integer which leaves remainder one when divided by three, then (1+ √3i)
n
+ (1- √3i)n
n
equals
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- 2n+1
0%
2n+1
0%
-(-2)n
0%
- 2n
The expression
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nπ + α
0%
2nπ
0%
nπ/2 + α
0%
None of these
If z
2
+ z + 1= 0, where z is a complex number, then then the value of
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0%
6
0%
12
0%
18
0%
24
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n cos ∅
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cos n∅
0%
n cos (n∅/2)
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sin (n∅/2)
If square root of -7 + 24i is x + iy then x is equal to
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± 1
0%
± 2
0%
± 3
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± 4
If is a complex cube root of unity, then
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1/√2
0%
1/2
0%
1
0%
√3/2
The value of
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0%
0
0%
-1
0%
i
0%
1
If ω is an imaginary cube root of unity and x = a + b, y = aω + bω
2
, z = aω
2
+ bω, then x
2
+ y
2
+ z
2
is equal to
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0%
6ab
0%
3ab
0%
6a2b2
0%
3a2b2
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0%
1
0%
√2
0%
2√2
0%
4
0%
8
If ω is a cube root of unity then the value of (1 - ω + ω
2
)
5
+ (1 - ω - ω
2
)
5
is
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0%
30
0%
32
0%
2
0%
None of these
The principal amplitude of (sin 40
o
+ i cos 40
o
)
5
is
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0%
700
0%
-1100
0%
1100
0%
-700
The modulus and amplitude of (1+ i√3 )
8
are respectively
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256 and π/3
0%
256 and 2π/3
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256 and 2π/3
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256 and 8π/3
If 2x = -1+ √3i, then the value of (1- x
2
+ x)
6
- (1- x + x
2
)
6
is
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0%
32
0%
-64
0%
64
0%
0
The square roots of - 7 - 24√-1 are
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0%
± (4 + 3√-1)
0%
±(3 + 4√-
0%
±(3 - 4√-1)
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±(4 - 3√-
If 1, ω and ω
2
are the cube roots of unity, then , is equal to (1+ω) (1+ ω
2
) (1 + ω)
4
(1+ ω
8
) is equal to
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1
0%
0
0%
ω2
0%
ω
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0%
0%
2)
0%
(x + y + z)i
0%
π
0%
If 1 + x
2
=√3x then
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0%
0
0%
48
0%
-24
0%
24
0%
-48
If ω (#is a cube root of unity and (1+ ω
2
)
n
= (1+ ω
4
)
n
, then the least positive value of n is
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0%
2
0%
3
0%
5
0%
6
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0%
0
0%
1
0%
- 1
0%
None of these
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0%
1
0%
0
0%
- 1
0%
None of these
A value of n such that
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0%
12
0%
3
0%
2
0%
1
If 1, ω and ω
2
are the cube roots of unity, then (1 - ω + ω
2
)(1 - ω
2
+ ω
4
)(1 - ω
4
+ ω)
8
(1 - ω
8
+ ω
16
) ... up to 2n factors is
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0%
2n
0%
22n
0%
1
0%
- 22n
If 1, a
1
, a
2
,...a
n-1
are the nth roots of unity, then the value of (1-a
1
) (1 - a
2
)(1 - a
3
)...(1 - a
n-1
) is
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0%
√3
0%
1/2
0%
n
0%
0
One root of (1)
1/3
is
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0%
0%
2)
0%
0%
If iz
4
+ 1 = 0, then z can take the value
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0%
0%
cos π/8 + i sin π/8
0%
1/4i
0%
i
If i = √-1, then
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0%
1 - i√-3
0%
-1 + i√-3
0%
i√3
0%
-i√3
0%
1 + i√3
If a = e
i(2π/3)
, then the equation whose roots are a + a
-2
and a
2
+ a
-4
is
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x2 -2x + 4 = 0
0%
x2 - x + 1 = 0
0%
x2 + x + 4 = 0
0%
x2 + 2x - 4 = 0
0%
x2 + 2x + 4 = 0
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0%
2
0%
zero
0%
- 1
0%
1
If ω is an imaginary cube root of unity, then (1+ ω - ω
2
)
7
equals
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0%
128ω
0%
-128ω
0%
128ω2
0%
- 128ω2
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0%
16
0%
-16
0%
16ω
0%
16ω2
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0%
0
0%
- 1
0%
1
0%
i
The minimum value of |a + bω + cω
2
|, where a, b and c are all not equal integers and ω(≠1)is a cube root of unity, is
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0%
√3
0%
1/2
0%
1
0%
0
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0%
1
0%
ω
0%
ω2
0%
0
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1 but not 1
0%
-1 but not 1
0%
+1 or -1
0%
0
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0%
27
0%
27i
0%
214 i
0%
- 27 i
0%
-2 14
If 1, ω and ω
2
are the cube roots of unity, then ω(1+ ω)
3
— (1+ ω
2
) is equal to
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0%
1
0%
- 1
0%
i
0%
0
If x = α + β, y = αω + βω
2
, z = aω
2
+βω, βω is an imaginary cube root of unity. Then, the value of xyz is
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0%
α2 + β2
0%
α2 - β2
0%
α 3 + β3
0%
α3 - β3
Which of the following is a fourth root of 1/2 + i √3/2 ?
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0%
cos π/12
0%
cos π/2
0%
cos π/6
0%
cos π/3
If 1, ω and ω
2
are the cube roots of unity, (3 + ω
2
+ω
4
)
6
is equal to
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0%
64
0%
729
0%
2
0%
0
Let complex numbers a and 1/a lie on circles (x —x
0
)
2
+(y —y
0
)
2
= r
2
and (x - x
0
)
2
( y - y
0
)
2
4r
2
, respectively. If z
0
= x
0
+ iy
0
satisfies the equation 2|z
0
|
2
= r
2
+ 2, then |a|is equal to
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1/√2
0%
1/2
0%
1/√7
0%
1/3
If z is a complex such that |z| ≥ 2, then the minimum value of |z + 1/2|
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(a) is equal to 5/2
0%
(b) lies in the interval (1, 2)
0%
(c) is strictly greater than 5/2
0%
(d) is strictly greater than 3/2 but less than 5/2
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