Complex Numbers And Quadratic Equations CBSE Questions & Answers

Complex Numbers And Quadratic Equations

This is Mathematics Class 11 Complex Numbers and Quadratic Equations CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(x + {1 \over x} = 2cos\alpha ,then,{x^n} - {1 \over {{x^n}}}\)
  • A
    none of these
  • B
    -2i sin \({\rm{n}}\alpha \)
  • C
    2i \({\rm{sin}}\alpha {\rm{or}} - {\rm{2i sin n}}\alpha \)
    Correct
  • D
    2i \({\rm{sinn}}\alpha \)
2
Square roots of i are
  • A
    \( \pm {1 \over {\sqrt 2 }}(1 + i)\)
    Correct
  • B
    \( \pm {1 \over {\sqrt 2 }}(1 - i)\)
  • C
    \( \pm 1\)
  • D
    none of these
3
The value of \({1 \over {1 + \omega }} + {1 \over {1 + {\omega ^2}}} = \)
  • A
    none of these
  • B
    0
  • C
    -1
  • D
    1
    Correct
4
The values of x and y \(\in \) R for which the numbers \( - 3 + {x^2}yi,{x^2} + y + 4i\) are conjugates of each other are
  • A
    -1 , -4
  • B
    none of these
  • C
    \( \pm 1, - 4\)
    Correct
  • D
    1 , -4
5
If \(x = {\omega ^2} - \omega - 3,\omega \) being a non real cube root of unity , then the value of \({x^4} + 6{x^3} + 10{x^2} - 12x - 19\) is
  • A
    none of these
  • B
    12
  • C
    5
    Correct
  • D
    19
6
Square roots of - 48 – 14 i are
  • A
    none of these
  • B
    \( \pm (1 + 7i\))
  • C
    \((1 - 7i\))
  • D
    \( \pm (1 - 7i\))
    Correct
7
The region of Argand’s plane represented by the inequality \({\text{| 1}} - {\text{ z | }} \leq {\text{ | 1 }} + {\text{ z |}}\) is
  • A
    Re ( z ) \(≥\) 0
    Correct
  • B
    Im ( z ) \(> \)0
  • C
    Re ( z ) \(≤ \)0
  • D
    none of these
8
If z is purely real and Re ( z) \(>\) 0 , then Amp. ( z ) is
  • A
    - \(\pi \)
  • B
    \(\pi \)
  • C
    none of these
  • D
    0
    Correct
9
If z is purely real and Re ( z) \(<\) 0 , then Arg . ( z ) is
  • A
    -\(\pi \)
  • B
    0
  • C
    none of these
  • D
    \(\pi \)
    Correct
10
Arg. ( 0 + 0 i )
  • A
    \(\pi \)
  • B
    0
  • C
    -\(\pi \)
  • D
    none of these
    Correct
11
Amp. (i)
  • A
    \({\pi \over 2}\)
    Correct
  • B
    0
  • C
    -\({\pi \over 2}\)
  • D
    none of these
12
Amp.( - i )
  • A
    -\({\pi \over 2}\)
    Correct
  • B
    \({\pi \over 2}\)
  • C
    \(\pi \)
  • D
    none of these
13
Amp. ( -1 – i )
  • A
    none of these
  • B
    3 \(\pi /{\rm{4}}\)
  • C
    -3 \(\pi /{\rm{4}}\)
    Correct
  • D
    \(\pi /{\rm{4}}\)
14
If z is any complex number, then \({{z - \bar z} \over {2i}}\) is
  • A
    purely imaginary
  • B
    either 0 or purely imaginary
  • C
    purely real
    Correct
  • D
    none of these
15
Which of the following is correct ?
  • A
    none of these.
    Correct
  • B
    {tex}{\text{1 }} + {\text{i }} < {\text{ 1}} - {\text{ i}}{tex}
  • C
    \({\text{3 }} - {\text{4i }} < {\text{ 2 }}--{\text{ 3i}}\)
  • D
    \({\text{2 }} + {\text{ 3i }} < {\text{ 3 }} + {\text{ 4i}}\)