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
The complex numbers z = x + iy which satisfy the equation \(\left| {{{z - 3i} \over {z + 3i}}} \right| = 1\) lie on
  • A
    None of these
  • B
    a circle passing through the origin
  • C
    the x-axis
    Correct
  • D
    the straight line y = 3
2
The inequality \({\text{| z }} - {\text{ 4 | }} < {\text{ | z }} - {\text{2 |}}\) represents the region given by
  • A
    none of these
    Correct
  • B
    none of these
  • C
    Re (z) \(<\) 0
  • D
    Re(z) \(>\)0
3
If x = \({{\sqrt 3 } \over 2} + {i \over 2},\) \({x^3}\) then equals
  • A
    1
  • B
    i
    Correct
  • C
    - i
  • D
    -1
4
\(2\sqrt { - 9} \sqrt { - 16,} \) is equals to
  • A
    -24
    Correct
  • B
    none of these
  • C
    24
  • D
    48
5
If \({\left( {\sqrt 3 + i} \right)^{10}} = a + ib;a,b \in R,\) then a and b are respectively :
  • A
    none of these
  • B
    128 and 128\(\sqrt 3 \)
  • C
    5 12 and - 512\(\sqrt 3 \)
    Correct
  • D
    64 and - 64\(\sqrt 3 \)
6
Let \(x,y \in R,\) hen x + iy is a non real complex number if
  • A
    y = 0
  • B
    x = 0
  • C
    x \( \ne \) 0
  • D
    y \( \ne \) 0
    Correct
7
Let \(x,y \in R,\) then x + iy is a purely imaginary number if
  • A
    x \( \ne \) 0 , y \( \ne \) 0
  • B
    x = 0 , y \( \ne \) 0
    Correct
  • C
    x = 0 , y = 0
  • D
    x \( \ne \) 0 , y = 0
8
Multiplicative inverse of the non zero complex number x + iy (\(x,y \in R,\))
  • A
    \({x \over {{x^{}} + {y^{}}}} - {y \over {{x^{}} + {y^{}}}}i\)
  • B
    \( - {x \over {{x^2} + {y^2}}} + {y \over {{x^2} + {y^2}}}i\)
  • C
    none of these
  • D
    \({x \over {{x^2} + {y^2}}} - {y \over {{x^2} + {y^2}}}i\)
    Correct
9
If \({z_{1}}and{z_2}\) are non real complex numbers such that \({z_1} + {z_{2}}and{z_1}{z_2}\) are real numbers , then
  • A
    none of these
  • B
    \({z_1} = \overline {{z_1}} \) and \({z_2} = \overline {{z_2}} \)
  • C
    \({z_1} = - \overline {{z_2}} \)
  • D
    \({z_1} = \overline {{z_2}} \)
    Correct
10
The inequality \({\text{| z }}--{\text{ 6 | }} < {\text{ | z }}--{\text{ 2 |}}\) represents the region given by
  • A
    Re(z) \(<\) 2
  • B
    Re(z) \(>\) 2
  • C
    Re(z) \(>\) 4
    Correct
  • D
    none of these
11
z + \(\overline {z} \ne 0\) if and only if
  • A
    z \( \ne \) 0
  • B
    \({\text{| z | }} \ne {\text{ }}0\)
  • C
    Im ( z ) \( \ne \)0
  • D
    Re(z) \( \ne \) 0
    Correct
12
Distance of the representative of the number 1 + I from the origin ( in Argand’s diagram ) is
  • A
    \(\sqrt 2 \)
    Correct
  • B
    2
  • C
    none of these
  • D
    1
13
If \(\omega \) is a cube root of unity , then \(\left( {1 + \omega } \right)\left( {1 + {\omega ^2}} \right)\left( {1 + {\omega ^4}} \right)\left( {1 + {\omega ^8}} \right).......\) upto 2n factors is
  • A
    -1
  • B
    1
    Correct
  • C
    none of these .
  • D
    0
14
Locus of z = 2 + i is given by :
  • A
    a straight lne parallel to y axis
    Correct
  • B
    none of these
  • C
    a circle
  • D
    a straight line parallel to x axis
15
If k , l, m , n are four consecutive integers , then \({i^k} + {i^l} + {i^m} + {i^n}\) is equal to :
  • A
    1
  • B
    0
    Correct
  • C
    4
  • D
    2