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Complex Numbers - Two Marks Study Materials

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Simplify \(\left( \cfrac { 1+i }{ 1-i } \right) ^{ 3 }-\left( \cfrac { 1-i }{ 1+i } \right) ^{ 3 }\)

  2. If z1=3-2i and z2=6+4i, find \(\cfrac { { z }_{ 1 } }{ z_{ 2 } } \)

  3. Find the modulus of the following complex numbers
    \(\cfrac { 2i }{ 3+4i } \)

  4. Find the square roots of 4+3i

  5. Show that the following equations represent a circle, and, find its centre and radius|
    \(\left| z-2-i \right| =3\)

  6. Find the principal argument Arg z , when z = \(\cfrac { -2 }{ 1+i\sqrt { 3 } } \)

  7. Evaluate the following if z=5−2i and w= −1+3i
    z−iw

  8. Write the following in the rectangular form:
     \(\overline { 3i } +\cfrac { 1 }{ 2-i } \).

  9. Find the modulus of the following complex numbers
    (1-i)10

  10. Show that the following equations represent a circle, and, find its centre and radius
    |3z-6+12i|=8

  11. Simplify the following:
     \(\sum _{ n=1 }^{ 102 }{ { i }^{ n } } \)

  12. Represent the complex numbe \(1+i\sqrt { 3 } \) in polar form.

  13. If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

  14. Find the modulus of the complex number i25.

  15. Find the values of the real number x and y if 3x + (2x - 3y) i = 6 + 3i9.

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