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12th Standard Maths Complex Numbers English Medium Free Online Test One Mark Questions 2020 - 2021

12th Standard

    Reg.No. :
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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. in+in+1+in+2+in+3 is

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    i

  2. If \(z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } } \) , then |z| is equal to 
     

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

  3. If |z-2+i|≤2, then the greatest value of |z| is

    (a)

    \(\sqrt { 3 } -2\)

    (b)

    \(\sqrt { 3 } +2\)

    (c)

    \(\sqrt { 5 } -2\)

    (d)

    \(\sqrt { 5 } +2\)

  4. z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

    (a)

    3

    (b)

    2

    (c)

    1

    (d)

    0

  5. The principal argument of (sin 40°+i cos40°)5 is

    (a)

    −110°

    (b)

    −70°

    (c)

    70°

    (d)

    110°

  6. The product of all four values of \(\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }\) is

    (a)

    -2

    (b)

    -1

    (c)

    1

    (d)

    2

  7. The value of (1+i) (1+i2) (1+i3) (1+i4) is

    (a)

    2

    (b)

    0

    (c)

    1

    (d)

    i

  8. If a=cosθ + i sinθ, then \(\frac { 1+a }{ 1-a } \) =

    (a)

    cot \(\frac { \theta }{ 2 } \)

    (b)

    cot θ

    (c)

    i cot \(\frac { \theta }{ 2 } \)

    (d)

    i tan\(\frac { \theta }{ 2 } \)

  9. If z=\(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) =

    (a)

    0

    (b)

    \(\frac{1}{2}\)

    (c)

    cot\(\frac { \theta }{ 2 } \)

    (d)

    \(\frac{1}{2}\)cot\(\frac { \theta }{ 2 } \)

  10. \(\frac { 1+e^{ -i\theta } }{ 1+{ e }^{ i\theta } } \) =

    (a)

    cosθ + i sinθ

    (b)

    cosθ - i sinθ

    (c)

    sinθ - i cosθ

    (d)

    sinθ + icosθ

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