Complex Numbers Test

Result

Complex Numbers Test - 16

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Weekly Quiz Competition

Question 1
4 / -1

If ω and ω² are the cube roots of unity, then roots of equation (x - 1)³ + 5 = 0 are

A
- 5, -5ω, - 5ω²

B
)- 4,1- 5ω,1- 5ω²

C
6,1- 5ω,1 + 5ω²

D
None of these

Solution
Question 2
4 / -1

If (√3i + 1)¹⁰⁰ =2⁹⁹ (a + ib), then a² + b² is equal to

A
4

B
3

C
2

D
0

Solution
Question 3
4 / -1

The value of (1+ √3i )⁴ + (1 - √3i)⁴ is

A
-16

B
16

C
14

D
-14

Solution
Question 4
4 / -1

If the fourth roots of unity are z₁, z₂ , z₃ and z₄ , then z²₁ + z²₂ + z²₃ + z²₄ is equal to

A
0

B
2

C
3

D
None of these

Solution
Question 5
4 / -1

A
(- 3, 0)

B
(0, 3)

C
(0, - 3)

D

Solution
Question 6
4 / -1

If ω # 1 is a cube root of unity, then the sum of the series S = 1+ 2ω+ 3ω² + • • • + 3ω^3n-1 is

A

B
3n(ω - 1)

C

D
0

Solution
Question 7
4 / -1

A
cos nθ - i sin nθ

B
cos nθ + i sin nθ

C
cos 2nθ - i sin 2nθ

D
cos 2nθ + i sin 2nθ

Solution
Question 8
4 / -1

If z = cos θ + i sin θ, then the value of

A

B

C

D

Solution
Question 9
4 / -1

If a is a complex number satisfying the equation α² + α + 1= 0, then α³¹ is equal to

A
α

B
α²

C
1

D
i

Solution
Question 10
4 / -1

The smallest positive integral value of n such that

A
4

B
3

C
2

D
8

Solution