If the complex numbers z1, z2, z3 and z4 denote the vertices of a

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 Multiple Choice QuestionsMultiple Choice Questions

291.

The region represented by z = x + iy  C : z - Rez  1 is also given by the inequality

  • y2  2x + 1

  • y2  x + 12

  • y2    2x +1

  • y2  x + 1


292.

If α and β be two roots of the equation x2 – 64x + 256 = 0. Then the value of α3β518 + β3α518 = ?

  • 2

  • 4

  • 4

  • 3


293.

If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to :

  • 2αα - 1

  • 2αα + 1

  • 2α2

  •  - 2αα + 1


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294.

If the complex numbers z1, z2, z3 and z4 denote the vertices of a square taken in order. If z1 = 3 + 4i and z3 = 5 + 6i, then the other two vertices z2 and z4 are respectively

  • 5 + 4i, 5 + 6i

  • 5 + 4i, 3 + 6i

  • 5 + 6i, 3 + 5i

  • 3 + 6i, 5 + 3i


B.

5 + 4i, 3 + 6i

Given, z1 = 3 + 4i

and     z3 = 5 + 6i

are two vertices of a square.

 Mid-point of diagonalz0 = 3 + 4i + 5 + 6i2 = 4 + 5i

since, diagonal of a square bisected each other.

Now by inspection, we get

z2 = 5 + 4i and z4 = 3 + 6i

        z0 = z2 + z42 = 4 +5i


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295.

If 1 + ix - i2 + i + 1 + 2iy + i2 - i = 1, then x, y =?

  • 73, - 715

  • 73, 715

  • 75, - 715

  • 75, 715


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