These Complex Numbers And Quadratic Equations Class 11 Solutions are most important for your upcoming examinations including JEE Main & JEE Advanced. These Complex Numbers And Quadratic Equations Class 11 Solutions will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.
Complex Numbers And Quadratic Equations Class 11 Solutions
1. If {(1 + i)/(1 – i)}n = 1 then the least value of n is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: 4
2. (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to
(A) 2n
(B) 22n
(C) 23n
(D) 24n
Answer: 22n
3. The value of √(-144) is
(A) 12i
(B) -12i
(C) ±12i
(D) None of these
Answer: 12i
4. The modulus of 5 + 4i is
(A) 41
(B) -41
(C) √41
(D) -√41
Answer: √41
5. If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are
(A) -1, -1 + 2ω, – 1 – 2ω²
(B) – 1, -1, – 1
(C) – 1, 1 – 2ω, 1 – 2ω²
(D) – 1, 1 + 2ω, 1 + 2ω²
Answer: – 1, 1 – 2ω, 1 – 2ω²
6. The value of x and y if (3y – 2) + i(7 – 2x) = 0
(A) x = 7/2, y = 2/3
(B) x = 2/7, y = 2/3
(C) x = 7/2, y = 3/2
(D) x = 2/7, y = 3/2
Answer: x = 7/2, y = 2/3
7. 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
Answer: θ = nπ ± π/3 where n is an integer
8. if x + 1/x = 1 find the value of x2000 + 1/x2000 is
(A) 0
(B) 1
(C) -1
(D) None of these
Answer: -1
9. Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Further assume that the origin, z1 and z1 form an equilateral triangle. Then
(A) a² = b
(B) a² = 2b
(C) a² = 3b
(D) a² = 3b
Answer: a² = 3b
10. The complex numbers sin x + i cos 2x are conjugate to each other for
(A) x = nπ
(B) x = 0
(C) x = (n + 1/2) π
(D) no value of x
Answer: no value of x
11. The real part of the complex number √9 + √(-16) is
(A) 3
(B) -3
(C) 4
(D) -4
Answer: 3
12. 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
Answer: line parallel to y-axis
13. The value of √(-4) *{√(-9/4)} is
(A) 3i
(B) -3i
(C) 3
(D) -3
Answer: -3
14. (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 )
Answer: 0 + 2b(3a2 – b2 )i/(a2 + b2 )
15. 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
Answer: Re (z) < 3
16. The value of {-√(-1)}4n+3 , n ∈ N is
(A) i
(B) -i
(C) 1
(D) -1
Answer: i
17. 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
Answer: 1 or – 1
18. 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
Answer: θ = nπ ± π/3 where n is an integer
19. The value of (1 – i)2 is
(A) i
(B) -i
(C) 2i
(D) -2i
Answer: -2i
20. The least value of n for which {(1 + i)/(1 – i)}n is real, is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: 2
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