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
Arg. ( x ) , x \(\in \) R and x \(<\) 0 is
  • A
    \(\pi /{\rm{2}}\)
  • B
    0
  • C
    \({\rm{3}}\pi /{\rm{2}}\)
  • D
    \(\pi \)
    Correct
2
The number of solutions of the equation \(Im\left( {{z^2}} \right) = 0,\left| z \right| = 2is\)
  • A
    4
    Correct
  • B
    1
  • C
    3
  • D
    2
3
Amp. \(\left( {{\rm{ z }}-{\rm{ 2 }}-{\rm{ 3 i }}} \right){\rm{ }} = {\rm{ }}\pi /{\rm{4}}\)then locus of z is
  • A
    x – y + 1 = 0
    Correct
  • B
    x – y = 2
  • C
    none of these
  • D
    x + y = 0
4
If \({z_{1}}and{z_2}\)are non real complex numbers such that \(\left| {{z_1}} \right| = \left| {{z_2}} \right|\) and Amp. \({z_{1}} + Amp.{z_2} = \pi \) , then
  • A
    none of these
  • B
    \( - \overline {{z_2}} \)
    Correct
  • C
    \(\overline {{z_2}} \)
  • D
    \({z_2}\)
5
The complex numbers sinx + i cos2x and cosx – i sin2x are conjugate to each other, for
  • A
    no value of x
    Correct
  • B
    none of these
  • C
    x = 0
  • D
    x = \({\rm{n}}\pi \)
6
The value of \({\left( { - 1 + \sqrt { - 3} } \right)^2} + {\left( { - 1 - \sqrt { - 3} } \right)^2}\)is
  • A
    -4
    Correct
  • B
    8
  • C
    4
  • D
    -2
7
If \(\alpha \) is a complex a number such that \({\alpha ^2} + \alpha + 1 = 0\) then \({\alpha ^{31}}\) is
  • A
    \(\alpha \)
    Correct
  • B
    0
  • C
    1
  • D
    \({\alpha ^2}\)
8
The value of \({\left( {{{1 + \omega } \over {{\omega ^2}}}} \right)^3}\) is
  • A
    none of these
  • B
    -1
    Correct
  • C
    0
  • D
    1
9
If n is any integer, then \({i^n}\) is
  • A
    1 , -1
  • B
    i
  • C
    1 ,-1 , i ,-i
    Correct
  • D
    none of the3se
10
The points z = x + iy which satisfy the equation \({\text{| z | }} = {\text{ 1}}\) lie on
  • A
    the circle whose centre is origin and radius = 1
    Correct
  • B
    the line y = 1
  • C
    the line x + y = 1
  • D
    the line x = 1
11
The equation \({z^2} = \bar zhas\)
  • A
    two solutions
  • B
    a unique solution
  • C
    four solutions
    Correct
  • D
    no solution
12
The points of the complex plane given by the condition arg. ( z ) = ( 2n + 1 ) \(\pi \), n \(\in \) I lie on
  • A
    the positive real semi axis z = x , x \(>\) 0
  • B
    the imaginary semi axis z = iy , y \(>\) 0
  • C
    the negative real semi axis z = x , x \(<\) 0
    Correct
  • D
    the imaginary semi axis z = iy , y \(<\) 0
13
If z = x + yi ; x ,y \(\in \) R, then locus of the equation\(\bar bz + b\overline {z} = c\), where c \(\in \) R and b \(\in \) C, b \( \ne \) 0 are fixed, is
  • A
    none of these
  • B
    a circle
  • C
    a parabola
  • D
    a straight line
    Correct
14
The complex number z which satisfies \(\left| {{{i + z} \over {i - z}}} \right| = 1,\)lies on
  • A
    the x - axis
    Correct
  • B
    none of these
  • C
    the line x + y =1
  • D
    the y - axis
15
\({\left( {1 + i} \right)^{2n}} + {\left( {1 - i} \right)^{2n}},n \in N,\)is
  • A
    a purely imaginary number
  • B
    a purely real number
    Correct
  • C
    none of these
  • D
    a non-real complex number