Complex Numbers &Quadratic Equations MCQs Part IV

1)
a) 2
b) 4
c) 6
d) none of these

2) The centre of a square is at the origin and is one of its vertices. The extremities of its diagonals which does not pass through this vertex are
a)
b)
c)
d) none of these

3) Let z and w be two complex numbers such that
a)
b)
c) 1 or -1
d)

4)
a) no solution
b) one solution
c) two solutions
d) none of these

5) If the area of the on the complex plane formed by the complex numbers , then the constant “a” is equal to
a) 1/2
b) 2/3
c) 3/4
d) none of these

6)
a) right angled but not isosceles
b) isosceles but not right angled
c) right angled and isosceles
d) equilateral

7)
a)
b)
c)
d)

8)
then

a)
b)
c)
d)

9)
a)
b)
c)
d) none of these

10)
a)
b)
c)
d)

11)
a)
b)
c)
d) none of these

12) The value of ii is
a)
b)
c)
d) none of these

13)
a) 2
b)
c) 0
d)

14) and e are
a) Natural numbers
b) Integers
c) Rational numbers
d) Irrational numbers

15) If then
a) z is purely real
b) z is purely imaginary
c) Real part of z = complex part of z
d) Z is any complex number

16) If and
are complex numbers, such that
+ is a real number, then

a)
b)
c)
d)

17) The number of solutions of the equation
is

a) 1
b) 2
c) infinitely many
d) 3

18) If, then which one of the following
is true

a)
b)
c)
d)

19) The conjugate of is
a)
b)
c)
d)

20) The principal value of the amplitude of (1+ i ) is
a)
b)
c)
d)

21) If n is any integer, then in is
a) I
b) 1, -1
c) i, -I
d) 1, -1, i, -i.

22) If b + ic = (1+ a) z and then
is equal to

a)
b)
c)
d)

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

24) If and
are two non-zero complex numbers such that
then is equal to

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

25) The points in complex plane
are the vertices of a parallelogram taken in order iff

a)
b)
c)
d)

26) If the cube roots of unity are ,
then roots of the equation are

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

27) The value of , is
a) -1
b) 0
c) -i
d) i

28)
is

a) a purely imaginary number
b) a purely real number
c) a non-real complex number
d) a complex number in which real and imaginary parts are equal

29) If is a non-real cube root of unity, then the linear factors of in complex numbers are
a)
b)
c)
d)

30) If , n integral, then lies on the unit circle for
a) only even n
b) only odd n
c) only positive n
d) all n

31) If the imaginary part of
is -2, then the locus of the point representing z in the complex plane is

a) circle
b) a st. line
c) a parabola
d) none of these

32) If z= x + iy and , then
= 1 implies that, in the complex plane

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

33) If, are non-real cube roots
of unity, then is equal to

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

34) If , then the value of
is

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

35) The real value of for which
the expression is purely real is

a)
b)
c)
d) none of these

36) The solution of the equation
is

a)
b) 3 – 2 i
c)
d)

37) Given that
and ,
then z =

a)
b)
c)
d)

38) If
a)
b)
c)
d) none of these

39) If z = x + iy such that 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

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

a) 0 if n is even
b)
c)
d) none of these

41) If , then the points representing
are

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

42) Suppose are the vertices of
an equilateral triangle circumscribing the circle .
If and
are in the clockwise sense, then

a)
b)
c)
d) none of these

43) , where z is non-real, can
be the angles of a triangle if

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

44) Which of the following is not applicable for a complex number?
a) Addition
b) Subtraction
c) Division
d) Inequality

45) The complex number
lies in

a) first quadrant
b) second quadrant
c) third quadrant
d) fourth quadrant

46) If z= -1, then the principal value of the arg
is equal to

a)
b)
c)
d)

47) The equation not representing a circle is given by
a)
b)
c)
d)

48) If is a complex root of unity,
then

a)
b)
c)
d)

49) If , then arg (z) is
a)
b)
c)
d)

50) If and arg ,
then z satisfies

a)
b)
c)
d)

51) The number is equal to
a) 1
b) -1
c) 2
d) -2

52) If
a)
b)
c)
d)

53) If are three complex numbers
in A.P., then they lie on

a) circle
b) a straight line
c) a parabola
d) an ellipse

54) If represent the vertices of
an equilateral triangle such that
then

a)
b)
c)
d)

55) For a positive integer n, the expression
equals

a) 0
b)
c)
d)

56) The smallest positive integer n for which
is

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

57) For , if
then and satisfy

a)
b)
c)
d)

58) If a complex number lies in the IIIrd quadrant then its conjugate
lies in quadrant number

a) I
b) II
c) III
d) IV

59) If z = x + iy lies in IIIrd quadrant then
also lies in the IIIrd quadrant if

a) x > y > 0
b) x < y < 0
c) y < x < 0
d) y > x > 0

60) If are two different complex
numbers such that , then the
expression equals

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

61) If is a complex cube root
of unity, then the product
to 2 n factors, is equal to

a)
b)
c)
d)

62) The values of x and y which satisfy the equation
are

a) x = 0 and y = 1
b) x =1 and y = 0
c) x = 3 and y = -1
d) x = -1 and y = 3

63) The square roots of 3-4 i are
a)
b)
c)
d)

64) A value of is
a) 0
b)
c) -i
d) I

65) If , then xyz equals
a)
b)
c)
d)

66) If are the three cube
roots of unity and and
ar

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

67) If z is a complex number, then
a)
b)
c)
d)

68) If z satisfies , then

a)
b)
c)
d)

69)
a) 2 + i
b) 2 – 10 i
c) -2 + i
d) -2 -10 i

70) The conjugate complex number of
is

a)
b)
c)
d)

71) The equation represents
a) a straight line
b) a circle
c) a parabola
d) a hyperbola

72) The value of is
a) 2
b) -2
c) 1
d) 0

73) tan is equal to
a) ab
b)
c)
d)

74) If is constant, then
the locus of z is

a)
b)
c)
d)

75) The value of
is

a)
b)
c)
d)

76) In the Argand diagram all the complex number z is satisfying
lie on a

a) st. line
b) circle
c) ellipse
d) parabola

77) If is an imaginary
cube root of unity, then
equals

a)
b)
c)
d)

78) The value of the sum
when equals

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

79) If then
a) x=3, y=1
b) x=1, y=3
c) x=0, y=3
d) x=0, y=0

80) If is equal to
a) -1
b) 1
c) -2
d) 2

81) If ,
then
is equal to

a)
b)
c)
d)

82) If z is any complex number satisfying ,
then which of the following is correct

a)
b)
c)
d)

83) The complex number
in polar form can be written as

a)
b)
c)
d)

84) If ,
then

a)
b)
c)
d)

85)
a)
b)
c) 1
d) -1

86) is possible if
a)
b)
c)
d)

87) ,
then
is equal to

a)
b)
c)
d)

88) If is the cube root
of unity, then

a) 4
b) 0
c) -4
d) none of these

89) If is the cube root
of unity of the equation ,
then the value of

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

90) If arg then
=

a)
b)
c)
d)

91) If are complex numbers
such that is equal to

a) 1
b) less than 1
c) greater than 1
d) equal to 3

92) The area of the triangle whose vertices are the points represented
by complex numbers z, iz, z+ iz is

a)
b)
c)
d)

93) The value of is
a) 1
b) 2
c)
d)

94) If , then the value
of cos will be

a)
b)
c)
d)

95) Let be nth roots of
units which subtends a right angle at the origin. Then n must be of
the form

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

96) If is purely imaginary
number

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

97) The value of is equivalent
to

a)
b)
c)
d) none of these

98) The value of is
a)
b)
c)
d) none of these

99) i57+ when simplified
has the value

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

100)
a) i
b) 2i
c) 1-i
d) 1-2i

Answers

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