NCERT Solutions for class 11 Maths | Chapter 5 - Complex Numbers and Quadratic Equations

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Questions
1 If arg (z) < 0, then arg (-z) – arg (z) =
A π
B -π
C -π/2
D π/2

Answer:π
2 The curve represented by Im(z²) = k, where k is a non-zero real number, is
A a pair of striaght line
B an ellipse
C a parabola
D a hyperbola

Answer: a hyperbola
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3 The value of i-999 is
A 1
B -1
C i
D -i

Answer:i
4 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
5 The value of √(-16) is
A -4i
B 4i
C -2i
D 2i

Answer:4i
6 If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equals
A 128 ω
B -128 ω
C 128 ω²
D -128 ω²

Answer:-128 ω²
7 Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =
A -2√3 + 2i
B 2√3 + 2i
C 2√3 – 2i
D -√3 + i

Answer:-2√3 + 2i
8 The value of √(-25) + 3√(-4) + 2√(-9) is
A 13i
B -13i
C 17i
D -17i

Answer:17i
9 if z lies on |z| = 1, then 2/z lies on
A a circle
B an ellipse
C a straight line
D a parabola

Answer:a circle
10 The value of √(-144) is
A 12i
B -12i
C ±12i
D None of these

Answer:12i
11 If {(1 + i)/(1 – i)}n = 1 then the least value of n is
A 1
B 2
C 3
D 4

Answer:4
12 (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
13 The value of √(-144) is
A 12i
B -12i
C ±12i
D None of these

Answer:12i
14 The modulus of 5 + 4i is
A 41
B -41
C √41
D -√41

Answer:√41
15 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
16 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
17 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
18 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
19 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
20 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

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