Objective Questions On Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

Questions

1 The real part of the complex number √9 + √(-16) is

A 3

B -3

C 4

D -4

View Answer

Answer:3

2 If z = x + iy, then | 3z - 1 | = 3 | z - 2 | represents

A x-axis

B y-axis

C a circle

D line parallel to y-axis

View Answer

Answer:line parallel to y-axis

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3 The value of √(-4) *{√(-9/4)} is

A 3i

B -3i

C 3

D -3

View Answer

Answer:-3

4 (a + ib)² /(a - ib) - (a - ib)² /(a + ib) in A + iB form is

A 0 + 2b(3a² - b² )i/(a² + b² )

B 1 + 2b(3a² - b² )i/(a² + b² )

C 2 + 2b(3a² - b² )i/(a² + b² )

D 3 + 2b(3a² - b² )i/(a² + b² )

View Answer

Answer:0 + 2b(3a² - b² )i/(a² + b² )

5 The inequality | z - 2 | < | z - 4 | represents the region given by

A Re (z) > 0

B Re (z) < 3

C Re (z) > 2

D none of these

View Answer

Answer:Re (z) < 3

6 The value of {-√(-1)}⁴ⁿ⁺³ , n ∈ N is

A i

B -i

C 1

D -1

View Answer

Answer:i

7 If z and w be two complex numbers such that | z | ≤ 1, | w | ≤ 1 and | z + iw | = | z - iw | = 2, then z equals {w is congugate of w}

A 1 or i

B i or - i

C 1 or - 1

D i or - 1

View Answer

Answer:1 or - 1

8 Find real θ such that (3 + 2i * sin θ)/(1 - 2i * sin θ) is imaginary

A θ = nπ ± π/2 where n is an integer

B θ = nπ ± π/3 where n is an integer

C θ = nπ ± π/4 where n is an integer

D None of these

View Answer

Answer:θ = nπ ± π/3 where n is an integer

9 The value of (1 - i)² is

A i

B -i

C 2i

D -2i

View Answer

Answer:-2i

10 The least value of n for which {(1 + i)/(1 - i)}ⁿ is real, is

A 1

B 2

C 3

D 4

View Answer

Answer:2

11 If the area of the triangle on the complex plane formed by the points z, izand z + iz is 50 square units, then |z| is

A 5

B 10

C 15

D None of these

View Answer

Answer:10

12 If z = x + iy and w = 1 - iz / z - i , then | w | = 1 implies that, in the complex plane,

A z lies on the imaginary

B z lies on the real axis

C z lies on the unit circle

D None of these

View Answer

Answer:z lies on the real axis

13 The argument of (1 - i√3)/(1 + i√3) is

A π/3

B 2π/3

C 7π/3

D 4π/3

View Answer

Answer:4π/3

14 The roots of the equation x² + x + 1 = 0 is

A {1 ± i√3}/2

B {-1 ± i√3}/2

C {i ± √3}/2

D {-i ± √3}/2

View Answer

Answer:{-1 ± i√3}/2

15 The value of i + i² + i³ + i⁴ is

A 0

B 1

C -1

D 2i

View Answer

Answer:0

16 If α is cube root of unity, then for n ∈ N, the value of α^{3n + 1} + α^{3n + 5} is

A -1

B 0

C 1

D 3

View Answer

Answer:-1

17 The inequality | z - 2 | < | z - 4 | represents the region given by

A Re (z) > 0

B Re (z) < 3

C Re (z) > 2

D none of these

View Answer

Answer:Re (z) < 3

18 Let z = a + ib and if |z| = 0 then

A Real(z) = 0

B Imaginary(z) = 0

C Real(z) = Imaginary(z) = 0

D None of these

View Answer

Answer:Real(z) = Imaginary(z) = 0

19 The equation whose roots are 7i and 2i is

A x² + (9i)x - 14 = 0

B x² - (9i)x + 14 = 0

C x² - (9i)x - 14 = 0

D x² + (9i)x + 14 = 0

View Answer

Answer:x² - (9i)x - 14 = 0

20 The locus of the point z satisfying Re(z2 ) = 0 is

A A pair of striaght line

B a circle

C a rectangular hyperbola

D None of these

View Answer

Answer:A pair of striaght line

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