Complex Numbers Two Marks Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. If z=x+iy, find the following in rectangular form.
    \(Re\left( \cfrac { 1 }{ z } \right) \)

  2. Represent the complex number −1−i

  3. Write the following in the rectangular form:
    \(\cfrac { 10-5i }{ 6+2i } \)

  4. Find the square roots of −6+8i

  5. Obtain the Cartesian form of the locus of z=x+iy in
    \(\overline { z } =2^{ -1 }\)

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

  7. Write in polar form of the following complex numbers
    \(3-i\sqrt { 3 } \)

  8. Simplify the following:
    i i2i3...i40

  9. Find the modulus and principal argument of the following complex numbers.
    \(-\sqrt { 3 } +i\)

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

  11. Find Re (z) and im (z) if z = 5i11 + 7i3

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

  13. If 1, ω, ω2 are the cube roots of unity show that (1+ω2)3 - (1+ω)3 =0

  14. Find the argument of -2

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

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