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

12th Standard

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Maths

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

    Answer all the questions

    10 x 1 = 10
  1. The value of \(\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) } \) is

    (a)

    1+ i

    (b)

    i

    (c)

    1

    (d)

    0

  2. If z is a non zero complex number, such that 2iz2=\(\bar { z } \) then |z| is

    (a)

    \(\cfrac { 1 }{ 2 } \)

    (b)

    1

    (c)

    2

    (d)

    3

  3. The solution of the equation |z|-z=1+2i is

    (a)

    \(\cfrac { 3 }{ 2 } -2i\)

    (b)

    \(-\cfrac { 3 }{ 2 } +2i\)

    (c)

    \(2-\cfrac { 3 }{ 2 } i\)

    (d)

    \(2+\cfrac { 3 }{ 2 } i\)

  4. If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is

    (a)

    1

    (b)

    i

    (c)

    x2+y2

    (d)

    1+n2

  5. The value of \(\left( \cfrac { 1+3\sqrt { i } }{ 1-\sqrt { 3i } } \right) ^{ 10 }\)

    (a)

    \(cis\cfrac { 2\pi }{ 3 } \)

    (b)

    \(cis\cfrac { 4\pi }{ 3 } \)

    (c)

    \(-cis\cfrac { 2\pi }{ 3 }\)

    (d)

    \(-cis\cfrac { 4\pi }{ 3 }\)

  6. If \(\sqrt { a+ib } \) =x+iy, then possible value of \(\sqrt { a-ib }\) is

    (a)

    x2+y2

    (b)

    \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \)

    (c)

    x+iy

    (d)

    x-iy

  7. If z=cos\(\frac { \pi }{ 4 } \)+i sin\(\frac { \pi }{ 6 } \), then

    (a)

    |z| =1, arg(z) =\(\frac { \pi }{ 4 } \)

    (b)

    |z| =1, arg(z) =\(\frac { \pi }{ 6 } \)

    (c)

    |z|=\(\frac { \sqrt { 3 } }{ 2 } \), arg(z)=\(\frac { 5\pi }{ 24 } \)

    (d)

    |z| =\(\frac { \sqrt { 3 } }{ 2 } \), arg (z) =tan-1\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

  8. If x+iy =\(\frac { 3+5i }{ 7-6i } \), they y =

    (a)

    \(\frac { 9 }{ 85 } \)

    (b)

    -\(\frac { 9 }{ 85 } \)

    (c)

    \(\frac { 53 }{ 85 } \)

    (d)

    none of these

  9. If zn =\(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z1, z2 ..... z6 is

    (a)

    1

    (b)

    -1

    (c)

    i

    (d)

    -i

  10. The conjugate of \(\frac { 1+2i }{ 1-(1-i)^{ 2 } } \) is _______

    (a)

    \(\frac { 1+2i }{ 1-(1-i)^{ 2 } } \)

    (b)

    \(\frac { 5 }{ 1-(1-i)^{ 2 } } \)

    (c)

    \(\frac { 1-2i }{ 1+(1+i)^{ 2 } } \)

    (d)

    \(\frac { 1+2i }{ 1+(1-i)^{ 2 } } \)

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