Important Questions of Complex Numbers and Quadratic Equations Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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221.

The product of the distinct (2n)th roots of 1 + i3 is equal to :

  • 0

  • - 1 - i3

  • 1 + i3

  • - 1 + i3


222.

If α and β are the roots of the equation ax2 + bx + c = 0 and, if px2 + qx + r = 0 has roots 1 - αα and 1 - ββ, then r is equal to

  • a + 2b

  • a + b + c

  • ab + bc + ca

  • abc


223.

If 1, 2, 3 and 4 are the roots of the equation x4 + ax3 + bx2 + cx + d = 0, then a + 2b + c is equal to

  • - 25

  • 0

  • 10

  • 24


224.

If α, β, γ are the roots of x3 - 2x2 + 3x - 4 = 0, then the value of α2β2 + β2γ2 + γ2α2 is

  • - 7

  • - 5

  • - 3

  • 0


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225.

The locus of the point z = x + iy satisfying z - 2iz + 2i = 1 is  

  • x-axis

  • y-axis

  • y = 0

  • x = 2


226.

A value of n such that 32 +i2n = 1 is

  • 12

  • 3

  • 2

  • 1


 Multiple Choice QuestionsMatch The Following

227.

If a = 1 - i32, then the correct matching of List-I from List-II is

         List-I                       List-II

(i)      aa                            - π3

(ii)    arg1a                       - i3

(iii)    a - a                        2i3 

(iv)     Im43a                    1

                                        π3

                                        23

correct match is 

A. (i) (ii) (iii) (iv) (i) D E C B
B. (i) (ii) (iii) (iv) (ii) D A B F
C. (i) (ii) (iii) (iv) (iii) F E B C
D. (i) (ii) (iii) (iv) (iv) D A B C

 Multiple Choice QuestionsMultiple Choice Questions

228.

The points in the set z  C : argz - 2z - 6i = π2 (where C denotes the set of all complex numbers) lie on the curve which is a

  • circle

  • pair of lines

  • parabola

  • hyperbola


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229.

If w is a complex cube root of unity, then sinw10 + w23π - π4 is equal to

  • 12

  • 12

  • 1

  • 32


230.

If m1, m2, m3 and m4 respectively denote the moduli of the complex numbers 1 + 4i, 3 + i, 1 - i and 2 - 3i, then the correct one, among the following is

  • m1 < m2 < m3 < m4

  • m4 < m3 < m2 < m1

  • m3 < m2 < m4 < m1

  • m3 < m1 < m2 < m4


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