Important Questions of Complex Numbers and Quadratic Equations Mathematics | Zigya

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41.

Let z, z2 and z3 be non-zero complex numbers satisfying

z2 = iz, where i =  - 1.

Consider the following statements :

  1. z1z2z3 is purely imaginary
  2. z1z2 + z2z3 + z3z1 is purely real

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


42.

Let, z be a complex number satisfying

z - 4z - 8 = 1 and zz - 2 = 32

What is z = ?

  • 6

  • 12

  • 18

  • 36


43.

Let, z be a complex number satisfying

z - 4z - 8 = 1 and zz - 2 = 32

What is z - 6z + 6 = ?

  • 3

  • 2

  • 1

  • 0


44.

Let α and β α < β be the roots of the equation x2 + bx + c = 0, where, b > 0 and c < 0

Consider the following :

1. β < - α2. β < α

Which of the above is/are correct ?

  • 1 only

  • 2 only

  • both 1 and 2

  • neither 1 nor 2


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45.

Let α and β α < β be the roots of the equation x2 + bx + c = 0, where, b > 0 and c < 0

Consider the following :

1. α + β + αβ > 02. α2β + β2α > 0

Which of the above is/are correct ?

  • 1 only

  • 2 only

  • both 1 and 2

  • neither 1 nor 2


46.

If one root of the equation (l - m)x2 + lx+ 1 = is double the other and l is real, then what is thgreatest value of ?

  •  - 98

  • 98

  • - 89

  • 89


47.

Suppose ω1 and  ω2, are two distinct cube roots of unitdifferent from 1. Then what is ω1 - ω22 equal t?

  • 3

  • 1

  •  - 1

  •  - 3


48.

Let  α and β be the roots of the equation :

x2 - 1 - 2a2x + 1 - 2a2 = 0

Under what condition does the above equation have real roots ?

  • a2 < 12

  • a2 > 12

  • a2  12

  • a2  12


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49.

Let  α and β be the roots of the equation :

x2 - 1 - 2a2x + 1 - 2a2 = 0

Under what condition 1α2 + 1β2 < 1 ?

  • a2 < 12

  • a2 > 12

  • a2 > 1

  • a2  13, 12 only


50.

What is 1 + ω21 + ω = ?, where ω is cube root of unity

  • 1

  • ω

  • ω2

  • None of the above


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