# Complex Numbers &Quadratic Equations MCQs Part III

1) For any two complex numbers and any two real numbers a and b,
a)
b)
c)
d) none of these

2) Let a be a complex number such that
be vertices of a polygon such that Then the vertices of the polygon lie within a circle

a)
b)
c)
d)

3) Common roots of the equations
and are

a)
b)
c)
d)

4) If are two complex numbers
such that then

a)
b)
c)
d) all the above

5) The cube roots of unity
a) are collinear
b)
c) from an equilateral triangle
d) none of these

6) If are two complex numbers
such that then

a)
b)
c)
d) none of these

7) If are two complex numbers such
that then the angle between

a)
b)
c)
d)

8) If n is a positive integer greater than unity and z is a complex number
satisfying the equation then

a) Re (z)<0
b) Re (z)>0
c) Re (z)=0
d) None of these

9) If n is a positive integer greater than unity and z is a complex number
satisfying the equation then

a) Im (z)<0
b) Im (z)>0
c) Im (z)=0
d) None of these

10) If at least one value of the complex number
satisfy the condition and
the inequality then

a) a>2
b) a=2
c) a<2
d) none of these

11) If are two complex numbers such that then the pair of complex numbers, satisfy
a)
b)
c)
d) all the above

12) Given z is a complex number with modulus 1. Then the equation

a) all roots, real and distinct
b) two real and two imaginary
c) three roots real and one imaginary
d) one root real and three imaginary

13) The centre of a regular polygon of n sides is located at the
point z=0, and one of its vertex
is known. If be the
is equal to

a)
b)
c)
d) none of these

14) If the points are the vertices of an equilateral triangle in the argand plane, then
a)
b)
c)
d) all the above

15) The origin and the roots of the equation
form an equilateral triangle if

a)
b)
c)
d)

16) If z is a complex number such that
then the locus of z is

a) x-axis
b) straight line y=5
c) a circle passing through the origin
d) none of these

17)
a) 5
b) 4
c) 6
d) none of these

18) For any complex number z, the minimum value of
a) 1
b) 3
c) 1/2
d) 3/2

19)
a) Re(z)>0
b) Re(z)<0
c) Re(z)>2
d) Re(z)>3

20) The cube roots of unity lie on a circle
a)
b)
c)
d) none of these

21) Number of non-zero integral solution of the equation

a) 1
b) 2
c) Infinite
d) None of these

22)
a) a circle
b) a parabola
c) a straight line
d) none of these

23)
a) 1
b) 2
c) 3
d) 5

24)
a) 0
b) -160
c) 160
d) -164

25) For any two complex numbers
a)
b)
c)
d) none of these

26)
are vertices of an equilateral triangle with

a)
b)
c)
d)

27)
are two complex numbers such that

a)
b)
c)
d) none of these

28)
a) a circle
b) a straight line
c) a pair of straight lines
d) none of these

29)
are affixes of the vertices A, B and C respectively of a triangle ABC having centroid at G such that z=0 is the mid point of AG, then

a)
b)
c)
d)

30)
a)
b)
c)
d) none of these

31) For any two complex numbers
a)
b)
c)
d)

32)
a)
b)
c)
d) none of these

33) be a complex number such that
a) Re(z)>1
b) Im(z)>1
c) Re(z)=1
d) Im(z)=1

34) If n is an integer other than a multiple of 3, then the value of
a) 1
b) -1
c) 0
d) 3

35) If g(x) and h(x) are two polynomials such that the polynomial
a) g(1)=h(1)=0
b) g(1)+h(1)=0
c) g(1)= -h(1)
d) all the above

36) The product of n nth roots of unity is
a) 1
b) -1
c)
d)

37)

a) 0
b) 1
c) -1
d) none of these

38) If p is a multiple of n, then the sum of pth powers of nth roots of unity
is

a) p
b) n
c) 0
d) none of these

39) If p is not a multiple of n, then the sum of pth powers of nth roots of
unity is

a) 0
b) 1
c) n
d) p

40)
a) 1
b) -1
c) 0
d) none of these

41) then value of

a)
b)
c)
d)

42)
a) 1
b) -1
c) i
d) -i

43) then
a) 1
b)
c) A+B
d)

44)
a)
b)
c)
d)

45) the cube root of p, p<0,
then for any x, y and z the values of

a)
b)
c) 1, -1
d) none of these

46) of an equilateral triangle
(a, b are real numbers between 0 and 1), then

a)
b)
c) a=1/2, b=3/4
d) none of these

47)
a) 1
b) 0
c) 2
d) -1

48) the affixes of the vertices
of a parallelogram taken in order in Argand plane, then

a)
b)
c)
d) none of these

49) If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c=(1-r)a+rb and w=(1-r)u+rv, where r is a complex number, then the two triangles
a) have the same area
b) are similar
c) are concurrent
d) none of these

50) The region of the Argand diagram defined by

a) interior of an ellipse
b) exterior of a circle
c) interior and boundary of an ellipse
d) none of these

51) If a complex number z lies on the interior or on the boundary of a circle
or radius 3 and centre at (-4,0), then the greatest and least values of

a) 5,0
b) 6,1
c) 6,0
d) none of these

52)
a)
b)
c)
d) none of these

53) anticlockwise sense, then
a)
b)
c)
d) none of these

54)
a) 0
b) 1
c) n
d) -n

55) minimum. Then z is equal to
a)
b)
c)
d) none of these

56)
a)
b)
c)
d)

57)
a)
b)
c)
d) 0

58)
a) origin
b)
c)
d)

59) If
a)
b)
c) 0
d)

60)
a) Conyclic
b) Vertices of a rectangle
c) Vertices of a rhombus
d) In a straight line

61) The value of
a) -1
b) 1
c) i
d) -i

62) If arg where a is a fixed number, then the locus of 2 is not given by
a) A straight line
b) circle with centre at the origin
c) circle with centre on y-axis
d) both a and c

63) If a is the nth root of unity, then
terms equal to

a)
b)
c)
d)

64) If
a) -i
b) i
c) 1
d) -1

65) If are two pairs of conjugate complex numbers, then arg
a) 0
b)
c)
d)

66) If m, n, p, q are consecutive integers then the value of
a) 1
b) 4
c) 0
d) none of these

67)
a)
b)
c)
d) none of these

68) If one vertex of a square whose diagonals intersect at the origin is
a)
b)
c)
d) none of these

69) The value of z satisfying the equation
a)
b)
c)
d) 0

70) Given that the real parts of
Then

a)
b)
c)
d) none of these

71)
a) n
b)
c) 0
d) none of these

72)
a)
b)
c)
d) none of these

73) n nth roots of unity , then for k=1,2,…..,n
a)
b)
c)
d)

74)
a) 0, 1
b) 1, 1
c) 1, 0
d) -1, 1

75) Let z and w be two non-zero complex numbers such that
a) w
b) -w
c)
d)

76)
a) Re(z)=Im(z) only
b) Re(z)=Im(z)>0
c)
d) none of these

77) the curve
a)
b)
c)
d) none of these

78)
a)
b)
c)
d)

79)
a)
b)
c)
d) none of these

80)
a) 1
b)
c)
d) 0

81)
a) 1
b) -1/2
c)
d) -1

82)
a)
b)
c)
d)

83)
a) 4
b) 8
c) 2
d) 12

84)

85)
a) 0
b) 1/2
c) 1
d) 2

86)
a) x=-3, y= -1
b) x=3, y= -1
c) x=3, y=1
d) x= -1, y=3

87)
a) -8
b) 8i
c) 8
d) 32

88)
a)
b)
c) 1
d) -1

89)
a)
b)
c)
d)

90)
a) -1
b) 0
c) 1
d) 2i

91) Area of the triangle formed by 3 complex numbers
a) 1/2
b) 1
c)
d) 2i

92)
a) 0
b) 6
c) 64
d) 128

93)
a) i
b)
c) 1
d) 2

94)
a) 3/2
b) -3/2
c) 0
d) 1

95)
a)
b)
c)
d)

96) The general value of which satisfies
the equation

a)
b)
c)
d)

97)
a)
b)
c)
d) none of these

98)
a) i
b)
c) 1
d) -1

99) Let A,B and C represent the complex numbers respectively
on the complex pane. If the circumcentre of the triangle ABC lies at the origin,then the orthocentre is represented by the complex number

a)
b)
c)
d)

100)
a) 4 solutions
b) 3 solutions
c) 2 solutions
d) 1 solution