Practice Test for Complex number | nda maths test | free test for maths

Question no. 1

Suppose, ω and ω₂ are two distinct cube roots of unity different from 1. Then, what is (ω₁ - ω₂)² equal to?
3
  1
  -1
  -3

Question no. 2

What is the argument of the complex number (−1 − i) , where i = √(−1)?
  5π/4
  -5π/4
  3π/4
None of these

Question no. 3

What is one of the square roots of 3 + 4i, where i = √(−1)?
2+i
  2-i
  -2 + i
  -3 - i

Question no. 4

Consider the following statements I. ( ω¹⁰ +1)⁷ + ω = 0
II. ( ω¹⁰⁵ +1)¹⁰ = p¹⁰ for some prime number p,
where, ω ≠ 1 is a cubic root of unity.
Which of the above statement(s) is/are correct?
Only I
  Only II
  Both I and II
  Neither I nor II

Question no. 5

The origin and the roots of the equation z² + pz + q = 0 form an equilateral triangle, if
p² = q
p² = 3q
q² = 3p
q² = p

Question no. 6

The number of solutions of the equation z² = z is
  2
  3
  4
  None of these

Question no. 7

What is the value of 1 + i² + i⁴ + i⁶ +.... + i¹⁰⁰, where i = √(−1)?
  0
  1
  -1
  None of these

Question no. 8

If (a+ib)(c+id)(e+if)(g+ih) = A+iB , then (a² + b²)(c² + d²)(e² + f²)(g² + h²) is equal to
A² - B²
  A² + B²
  A⁴ + B⁴
  A⁴ - B⁴

Question no. 9

What is the value of (-i )⁴ⁿ⁺³ + (i⁴¹ + i^-259 )⁹ , where n ∈ N ?
0
  1
i
  -i

Question no. 10

If ω is a cube root of unity, then the value of (1+ ω - ω² ) ( 1 - ω + ω²) is equal to
1
0
  2
  4

Question no. 11

If ω is the imaginary cube root of unity, then what is (2- ω + 2ω²)²⁷ equal to?
3²⁷ω
-3²⁷ω²
  3²⁷
  -3²⁷

Question no. 12

If α is an nth root of unity other than unity itself, then the value of 1 + α + α² +....... α^n-1 is equal to
  0
  1
  -1
  None of these

Question no. 13

The points z₁ ,z₂ ,z₃ and z₄ in the complex plane are the vertices of a parallelogram taken in order if and only if
z₁ + z₄ = z₂ + z₃
  z₁ + z₃ = z₂ + z₄
  z₁ + z₂ = z₃ + z₄
  None of these

Question no. 14

If 2x = 3 + 5i, then what is the value of 2x³ + 2x² - 7x + 72 ?
4
-4
8
-8

Question no. 15

What is one of the square roots of 3 + 4i, where i = #8730;(−1)?
  2+i
  2-i
  -2 + i
  -3 - i

Question no. 16

What is the argument of (1 - sinθ ) + icosθ ?
π/2 - θ/2
  π/2 + θ/2
  π/4 - θ/2
  π/4 + θ/2

Question no. 17

If ( √3 + i) = 2⁹⁹ (a + ib) then a² + b² is equal to
  √2
  4
  √3
  None of these

Question no. 18

If z + z^-1 = 1, then z¹⁰⁰ + z^-100 is equal to
  i
  -i
  1
  -1

Question no. 19

( x³ − 1 ) can be factorised as
(x-1)(x - ω)( x + ω² )
  (x-1)(x - ω)( x - ω² )
  (x-1)(x + ω)( x + ω² )
  (x-1)(x + ω)( x - ω² )

Question no. 20

If z₁ and z₂ are complex numbers with|z₁ | = |z₂ | , then which of the following is/are correct?
I. z₁ = z₂
II. Real part of z₁ = Real part of z₂
III. Imaginary part of z₁ = Imaginary part of z₂
Select the correct answer using the code given below
  Only I
  Only II
  Only III
  None of these