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

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Questions
1 The real part of the complex number √9 + √(-16) is
A 3
B -3
C 4
D -4

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

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

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 )

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

Answer:Re (z) < 3
6 The value of {-√(-1)}4n+3 , n ∈ N is
A i
B -i
C 1
D -1

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

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

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

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

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

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

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

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

Answer:{-1 ± i√3}/2
15 The value of i + i2 + i3 + i4 is
A 0
B 1
C -1
D 2i

Answer:0
16 If α is cube root of unity, then for n ∈ N, the value of α3n + 1 + α3n + 5 is
A -1
B 0
C 1
D 3

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

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

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

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

Answer:A pair of striaght line

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