# Complex Numbers &Quadratic Equations MCQs Part I

1) The value of is
a) 4i
b) 8i
c) 16i
d) -16i

2) Given that real roots of and
are negative. Then the number
reduces to

a)
b)
c)
d) none of these

3) The complex number z satisfying the equations
is

a) 6
b)
c)
d) none of these

4) If where
then the ordered pair (x,y) is given by

a) (0,3)
b)
c) (-3,0)
d) (0,-3)

5) If amp. , then
a)
b)
c)
d) none of these

6) If where a, b, c are real,
then is

a)
b)
c)
d) none of these

7) If where z=1+2i, then
is equal to

a)
b)
c)
d) none of these

8) If and
are the roots of , then

a)
b)
c)
d)

9) If 1, be the roots of
then is equal to

a) 1 if n=3m+1
b) 1 if n=3m+2
c)
d) none of these

10) If the two circles (where
are real) intersect orthogonally, then

a)
b)
c)
d)

11) The algebraic sum of perpendicular distance from the points 1,
to the line (where b is real,
is nth root of unity) is

a)
b)
c)
d) none of these

12) If the imaginary part of the expression
be zero, then the locus of z is

a) a st. line parallel to x-axis
b) is a parabola
c) is a circle of radius 1 and centre (1,0)
d) none of these

13) The number of values of k for
which
is a perfect square is

a) 1
b) 2
c) 0
d) none of these

14) If
then the factors of the expression
are

a) real and different
b) real and identical
c) complex
d) none of these

15) Let ,
where ,
have the roots
such that
then

a)
b)
c) q>0
d) none of these

16) If
and ,
have a common root
then

a) a +b = 1
b)
c)
d) a+b-1=0

17) If
are the roots of the equation
then the equation
has a root

a)
b)
c) both (a) and (b)
d) none of these

18) If
are the roots of
and are
the roots of
then

a)
b)
c)
d) none of these

19) If the roots of the equation
are imaginary and the sum of the roots is equal to their product then a
is

a) -2
b) 4
c) 2
d) none of these

20) The equation
can have real solution for x if a belongs to the interval

a)
b)
c)
d) none of these

21) The equation
can have real solutions for x if a belongs to

a)
b)
c)
d) both a and c

22) If satisfied the inequation then a value exists for
a)
b)
c)
d) none of these

23) If
are roots of the equation
then

a)
b)
c)
d) none of these

24)
a) 3
b) 2
c) 4
d) None of the given

25) The area of the triangle formed by the complex numbers z , iz , z + iz in the arg and diagram is
a)
b)

| z |2

c)

2 | z |2

d) None of the given

26)
a) parabola
b) circle
c) pair of straight lines
d) None of the given

27)
a)
b)
c)
d) None of the given

28)
a) Re (z) = 0
b) lm (z) = 0
c) Re (z) > 0, lm (z) > 0
d) Re (z)> 0,lm (z) < 0

29)
a) z lies on imaginary axis
b) z lies on real axis
c) z lies on unit circle
d) none of the given

30) The value of the sum
a) i
b) i-1
c) – i
d) 0

31) The smallest positive integral value of n for which
is purely imaginary with positive imaginary part, is

a) 2
b) 3
c) 4
d) none of these

32) If
then
is equal to

a)
b)
c)
d)

33) If ,
the number of values of
for different
is

a) 3
b) 2
c) 4
d) 1

34) Im(z) is equal to
a)
b)
c)
d) none of these

35) The value of
is

a) i
b) 2(-1+5i)
c) 1-5i
d) none of these

36) sin
, where z is nonreal, can be the angle of a triangle if

a) Re(z)=1, Im(z)=2
b)
c) Re(z) + Im(z) = 0
d) none of these

37) The complex numbers sin x – i cos 2x and cos x – i sin 2x are conjugate
to each other for

a)
b) x = 0
c)
d) no value of x

38) If z is a complex number satisfying the relation
then z is

a)
b)
c)
d)

39) If
then z is

a)
b)
c)
d) none of these

40) If
are two nonzero complex numbers such that
then amp
is equal to

a)
b)
c) 0
d)

41) The complex number z is purely imaginary if
a)
b)
c)
d) none of these

42) If
such that
and amp
then

a)
b)
c)
d)

43) Let. Then arg z is
a)
b)
c)
d) none of these

44) If then the fundamental amplitude
of z is

a)
b)
c)
d) none of these

45) If then
a)
b)
c)
d) none of these

46) If z = x+iy satisfies amp (z-1) = amp (z+3i) then the value of (x-1): y
is equal to

a) 2:1
b) 1:3
c) -1:3
d) none of these

47) Let z be a complex number of constant modulus such that
is purely imaginary then the number of possible values of z is

a) 2
b) 1
c) 4
d) none of these

48) If is an imaginary cube root
of unity then equals

a)
b)
c)
d)

49) If is a nonreal cube root of
unity then the expression is equal
to

a) 0
b) 3
c) 1
d) 2

50) If and x = ky then k is
a)
b)
c)
d)

51) , where ,
is divisible by

a)
b)
c)
d)

52) The smallest positive integral value of n for which
is real is

a) 3
b) 6
c) 12
d) 0

53) If then,
where n is a multiple of 3, is

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

54) If is a nonreal cube root of
unity then is equal to

a) -1
b)
c) 0
d)

55) If , r = 0, 1, 2, 3, 4 then
is equal to

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

56) If then for
is

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

57) If then the least value
of n is

a) 3
b) 4
c) 6
d) none of these

58) If the fourth roots of unity are
then
is equal to

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

59) If has the nonreal complex
roots then the value of
is

a) -7
b) 6
c) -5
d) 0

60) If , the set of integers, then
n is a multiple of

a) 6
b) 10
c) 9
d) 12

61) If then amplitude of z is
a)
b)
c)
d)

62) If z is a nonreal root of then
is equal to

a) 0
b) -1
c) 3
d) 1

63) If is nonreal and
then the value of is equal
to

a) 4
b) 2
c) 1
d) none of these

64) If be two complex numbers then
is equal to

a)
b)
c)
d) none of these

65) The set of values of for which
will have a pair of conjugate
complex roots is

a) R
b) {1}
c)
d) none of these

66) Nonreal complex numbers z satisfying the equation
a)
b)
c)
d) none of these

67) For a complex number z, the minimum value of
is

a) 1
b) 2
c) 3
d) none of these

68) If then
is equal to

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

69) If is a non-real cube root of
unity then , is equal to

a) 1
b) 3
c) 0
d) none of these

70) If z be a complex number satisfying
then is equal to

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

71) Let be two unimodular complex
numbers such that Im If
then

a)
b)
c)
d)

72) If then
a) is less than 6
b) is more than 3
c) is less than 12
d) lies between 6 and 12

73) and
then the maximum value of is

a)
b) 7
c)
d) none of these

74) If
= max
then

a)
b)
c)
d) none of these

75) represents the region
given by

a) Re(z)>0
b) Re(z)<0
c) Re(z)>2
d) none of these

76) If then the region traced
by z is

a)
b)
c)
d)

77) represents
a) a circle
b) an ellipse
c) a straight line
d) none of these

78) If then
are represented by

a) three vertices of a triangle
b) three collinear points
c) three vertices of a rhombus
d) none of these

79) If A, B, C are three points in the Argand plane representing the complex
numbers such that ,
where , then
the distance of A from the line BC is

a)
b)
c) 1
d) 0

80) The roots of the equation are
represented by the vertices of

a) a square
b) an equilateral triangle
c) a rhombus
d) none of these

81) If Re then z is represented by
a point lying on

a) a circle
b) an ellipse
c) a straight line
d) none of these

82) The angle that the vector representing the complex number
makes with the positive direction of the real axis is

a)
b)
c)
d)

83) If represents the complex
number and its additive inverse respectively, then the complex equation of the circle with PPâ€™ as a diameter is

a)
b)
c)
d) none of these

84) If then the points
representing are

a) concyclic
b) vertices of a square
c) vertices of a rhombus
d) none of these

85) Suppose are the
vertices of an equilateral triangle inscribed in the circle .
If and
are in the clockwise sense then

a)
b)
c)
d) none of these

86) If amp then z represents a point on
a) a straight line
b) a circle
c) a pair of lines
d) none of these

87) If the roots of
represent the vertices of a
in the Argand plane then the area of the triangle is

a)
b)
c) 2
d) none of these

88) The equation represents

a) 5
b)
c)
d) none of these

89) Let and be
two nonreal complex cube roots of unity and
be the equation of a circle with
as ends of a diameter then the value of
is

a) 4
b) 3
c) 2
d)

90) Let . If the origin
and the nonreal roots of
form the three vertices of an equilateral triangle in the Argand
plane then is

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

91) The equation , can
represent an ellipse if k is

a) 1
b) 2
c) 4
d) none of these

92) The equation represents
a hyperbola if

a) -2<k<2
b) k>2
c) 0<k<2
d) none of these

93) Let OP .OQ = 1 and let O, P, Q be three collinear points. If O and Q represent
the complex numbers 0 and z then P represents

a)
b)
c)
d) none of these

94) Let , where t is a real parameter.
The locus of z in the Argand plane is

a) a hyperbola
b) an ellipse
c) a straight line
d) none of these

95) The area of the triangle whose vertices are ,
where and are
the nonreal cube roots of unity, is

a)
b)
c) 0
d)

96) The nonzero real value of x for which
is purely real is

 (i) (ii) 1 (iii) (iv) none of these

a) i and iii
b) ii and iii
c) i and iii
d) iv

97) If and
such that then

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

98) If is a complex constant such
that has a real root then
(i)
(ii)
(iii)
(iv) the absolute value of the real root is 1

a) i, ii and iii
b) ii , iii and iv
c) i, iii and iv
d) ii and iii

99) If amp
and then
(i) (ii) (iii) (iv) none
of these

a) i and ii
b) ii and iii
c) iii and iv
d) none of these

100) If is a nonreal cube root of unity then the value of is(i)real(ii) (iii)(iv) not real
a) i and ii
b) ii and iii
c) iii and iv
d) none of these