Important Questions of Complex Numbers and Quadratic Equations Mathematics | Zigya

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211.

If z1, z2 are two complex numbers satisfying z1 - 3z23 - z1z2 = 1, z1  3, then z2 is equal to

  • 1

  • 2

  • 3

  • 4


212.

The value of n = 02i3n is

  • 9 + 6i13

  • 9 - 6i13

  • 9 + 6i

  • 9 - 6i


213.

The roots of the equation x - 3x - 2 = 0 are

  • - 1, - 1, 2

  • - 1, 1, - 2

  • - 1, 2, - 3

  • - 1, - 1, - 2


214.

If α, β, γ are the roots of x3 + 2x2 - 3x - 1 = 0 then α- 2 + β- 2 + γ- 2 = 

  • 12

  • 13

  • 14

  • 15


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215.

If α1, α2, α3 respectively denote the moduli of the complex number - i, 13(1 + i) and - 1 + i, 3 then their increasing order is

  • α1, α2, α3

  • α3, α2, α1

  • α2, α1, α3

  • α3, α1, α2


216.

If α is a  non-real root of x6 = 1, then α5 + α3  + α + 1α2 + 1 is equal to,

  • α2

  • 0

  • - α2

  • α


217.

The difference between two roots of the equation x3 - 13x2 + 15x + 189 = 0 is 2. Then  the roots of the equation are :

  • - 3, 5, 7

  • - 3, - 7, - 9

  • 3, - 5, 7

  • - 3, - 7, 9


218.

If α, β, γ are the roots of the equation x3 - 6x2 + 11x + 6 = 0,then  α2β + αβ2 is equal to:

  • 80

  • 84

  • 90

  • - 84


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219.

The locus of the point z = x + iy satisfying the equation

z - 1z + 1 = 1 is given by :

  • x = 0

  • y = 0

  • x = y

  • x + y = 0


220.

The equation of the locus of z such that z + iz - i = 2, where z= x + iy is a complex number, is

  • 3x2 + 3y2 + 10y - 3 = 0

  • 3x2 + 3y2 + 10y + 3 = 0

  • 3x2 - 3y2 - 10y - 3 = 0

  • x2 + y2 - 5y + 3 = 0


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