Complex Numbers One Mark Question

12th Standard EM

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Maths

Time : 00:30:00 Hrs
Total Marks : 10
    5 x 1 = 5
  1. in+in+1+in+2+in+3 is

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    i

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

    (a)

    1+ i

    (b)

    i

    (c)

    1

    (d)

    0

  3. The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

    (a)

    \(\cfrac { 1 }{ 2 } \left| z \right| ^{ 2 }\)

    (b)

    |z|2

    (c)

    \(\cfrac { 3 }{ 2 } \left| z \right| ^{ 2 }\)

    (d)

    2|z|2

  4. The principal value of the amplitude of (1+i) is

    (a)

    \(\frac { \pi }{ 4 } \)

    (b)

    \(\frac { \pi }{ 12 } \)

    (c)

    \(\frac { 3\pi }{ 4 } \)

    (d)

    \(\pi \)

  5. The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\)  is a positive integer is

    (a)

    16

    (b)

    8

    (c)

    4

    (d)

    2

  6. 5 x 1 = 5
  7. z is imaginary

  8. (1)

    |z1| |z2|

  9. |z|

  10. (2)

    ≤ |z1| + |z2|

  11. |z1 + z2|

  12. (3)

    |\(\bar { z } \)|

  13. |z1 - z2|

  14. (4)

    ≥ |z1| + |z2|

  15. |z1z2|

  16. (5)

    z=-\(\bar { z } \)

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