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
\(Amp.\left( {\sin {{6\pi } \over 5} + i\left( {1 + \cos {{6\pi } \over 5}} \right)} \right)\)is equal to
  • A
    \({{9\pi } \over {10}}\)
    Correct
  • B
    \({{5\pi } \over 6}\)
  • C
    \({{6\pi } \over 5}\)
  • D
    none of these
2
If \(z = {{\sqrt 3 + i} \over 2},\) then \({z^{69}}\) is equal to
  • A
    1
  • B
    i
  • C
    -i
    Correct
  • D
    none of these
3
If \(\omega \) is a cube root of unity , then the linear factors of \({x^3} + {y^3}\) in complex numbers are
  • A
    \(\left( {x + y} \right)\left( {x - y\omega } \right)\left( {x - y{\omega ^2}} \right)\)
  • B
    \(\left( {x + y} \right)\left( {x + y\omega } \right)\left( {x + y{\omega ^2}} \right)\)
    Correct
  • C
    \(\left( {x + y} \right)\left( {x + y\omega } \right)\left( {x - y{\omega ^2}} \right)\)
  • D
    \(\left( {x - y} \right)\left( {x + y\omega } \right)\left( {x + y{\omega ^2}} \right)\)
4
\(\left( {z + 1} \right)\left( {\overline z + 1} \right)\) can be expressed as
  • A
    none of these
  • B
    \({\left| {z + 1} \right|^2}\)
    Correct
  • C
    \(\left| {{z^2}} \right| + 1\)
  • D
    \(\left| {{z^2}} \right| + 2\)
5
If \(\alpha {\rm{ }},{\rm{ }}\beta \) are non-real cube roots of unity then \(\alpha \beta \) + \({\alpha ^5} + {\beta ^5}\) equals
  • A
    0
    Correct
  • B
    3
  • C
    1
  • D
    -1
6
The complex numbers z = x + iy ; x , y \(\in \) R which satisfy the equation \(\left| {{{z - 3i} \over {z + 3}}} \right| = 1\) lies on
  • A
    the line x + y = 0
    Correct
  • B
    the x axis
  • C
    the y axis
  • D
    the line parallel to y axis
7
If \(\alpha {\text{ and }}\beta \) are non real cube roots of unity, then which one of the following statements is incorrect:
  • A
    \({\beta ^2} = \alpha \)
  • B
    \(\alpha {\beta ^2} = 1\)
    Correct
  • C
    none of these
  • D
    \({\alpha ^2} = \beta \)
8
If z = \(\bar z\) , then
  • A
    z is a complex number
  • B
    z is purely real
    Correct
  • C
    z is purely imaginary
  • D
    none of these
9
The complex number \({{{{\left( {1 + i} \right)}^n}} \over {{{\left( {1 - i} \right)}^{n - 2}}}}\) is equal to
  • A
    \(2{i^{n - 4}}\)
  • B
    none of these
  • C
    \(4{i^{n - 2}}\)
  • D
    \(2{i^{n - 1}}\)
    Correct
10
The least value of n for which \({\left( {{{2i} \over {1 + i}}} \right)^n}\) is a positive integer is
  • A
    1
  • B
    2
  • C
    8
    Correct
  • D
    4
11
If \(\left( {x + iy} \right)\left( {p + iq} \right) = \left( {{x^2} + {y^{2}}} \right)i,then\)
  • A
    p = x , q = y
  • B
    p = ix , q = 0
  • C
    p = y , q = x
    Correct
  • D
    none of these
12
If z = x + yi and w = \({{1 - iz} \over {z - i}},then\left| w \right|\) = 1 implies that, in the complex plane
  • A
    z lies on the real axis
    Correct
  • B
    z lies on the imaginary axis
  • C
    z lies on the unit circle
  • D
    none of these
13
If \({p^2}\) - p + 1 = 0, then, the value of \({p^{3n}}is\) equal to
  • A
    -1
  • B
    1 or -1
    Correct
  • C
    1
  • D
    0
14
The solution of the equation \({\text{| z | }} = {\text{ z }} + {\text{ 1 }} + {\text{ 2i}}\) is
  • A
    3 – 2i
  • B
    none of these
  • C
    3/2 + 2i
  • D
    3/2 – 2i
    Correct
15
\({\text{a }} + {\text{ ib}} \leq {\text{ c }} + {\text{ id}}\) is meaningful only when
  • A
    \({a^2} + {d^{2}} = 0\)
  • B
    \({b^2} + {d^{2}} = 0\)
    Correct
  • C
    \({b^2} + {c^{2}} = 0\)
  • D
    none of these