Complex Numbers &Quadratic Equations MCQs Part II

1) If z is a nonzero complex number then
is equal to (i)(ii)
1(iii)
(iv)none of these

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

2) If z is a complex number satisfying
then
has the valuei)(ii)(iii)(iv) 0 when n is not a multiple of 3

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

3) The value of
and is a nonreal cube root of unity, is(i)3 if n is a multiple of 3(ii)-1 if n is not a multiple of 3(iii)2 if n is a multiple of 3(iv)none of these

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

4) If are roots of the equation
where
and are real, then

(i) (ii)
(iii)

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

5) The value of
and
is a nonreal fourth root of unity, is

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

6) Let x be a nonreal complex number satisfying
then x is(i) (ii) (iii)(iv) none of these

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

7) If
then
(i) Re(z) = 2Im(z)(ii)Re(z) + 2Im(z) = 0(iii) (iv) amp z = tan

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

8) If
are two complex numbers then(i) (ii)(iii)(iv)

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

9) Let be two complex numbers represented by points on the circle
and respectively
then(i) (ii) (iii) (iv) none of these

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

10) ABCD is a square, vertices being taken in the anticlockwise sense. If A
represents the complex number z and the intersection of the diagonals is the
origin then

(i) B represents the
complex number iz
(ii)
(iii) (iv) D represents the complex number
–iz

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

11) If
where
is a complex constant, then z is represented by a point on

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

12)

If
are the four complex numbers represented by the vertices of a quadrilateral
taken in order such that
and amp
then the quadrilateral is a

(i) rhombus (ii) square
(iii) rectangle (iv) a cyclic quadrilateral

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

13) If
and
are represented by the vertices of an equilateral triangle then

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

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

14) Let A,B, C be three collinear points which are such that AB. AC = 1
and the points are represented in the Argand plane by the complex numbers
0,
respectively. Then

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

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

15)

If
are represented by the vertices of a rhombus taken in the anticlockwise
order then

(i)
(ii)
(iii) (iv)

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

16) If amp
and
then

a)
b)
c)
d) none of these

17) If
then

a)
b)
c)
d) none of these

18) Let
Then

(i) (ii) amp
(iii) (iv)

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

19) If
then

(i) (ii)
(iii) (iv)

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

20) If, where x and y are reals,
then the ordered pair (x,y) is given by

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

21) , then (x,y)=
a)
b)
c)
d) none of these

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

23) If the area of the triangle on the complex plane formed by the points z, iz
and z+iz is 50 square units, then is

a) 5
b) 10
c) 15
d) none of these

24) If the area of the triangle on the complex plane formed by complex
numbers z,

a) 4
b) 2
c) 6
d) 3

25) The locus of point z satisfying Re
where k is a non-zero real numbers, is

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

26) The locus of point z satisfying
= 0 is

a) a pair of straight lines
b) a rectangular hyperbola
c) a circle
d) none of these

27) The curve represented by Im (z
=k, where k is a non-zero real number, is

a) a pair of straight lines
b) an ellipse
c) a parabola
d) a hyperbola

28) If z lies on
then 2/z lies on

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

29) The maximum value of
when z satisfies the condition
is

a)
b)
c)
d)

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

31) If
then the points representing the complex numbers -1+4z lie on a

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

32) The point representing the complex number z for which arg
lies on

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

33)
a) 0
b)
c)
d) none of these

34) If then
z lies on a

a) circle
b) a parabola
c) an ellipse
d) none of these

35)
a)
b) Re(z) <0
c) Im(z) >0
d) None of these

36) If the number
is purely imaginary, then

a)
b)
c)
d)

37) The curve represented by
where k=R such that
is

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

38) The number of solutions of the equation
is

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

39) if 1,are
the nth roots of unity and n is an odd natural number than

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

40) If 1,
are the nth roots of unity and n is even natural number, then

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

41) If z is a complex number having least absolute value and
then z=

a)
b)
c)
d)

42) The value of
is equal to (
is an imaginary cube root of unity).

a) 0
b)
c)
d)

43) The region in the Argand diagram defined by
is the interior of the ellipse with major axis along

a) the real axis
b) the imaginary axis
c) y=x
d)

44) The value,
where
is an imaginary cube root of unity, is

a)
b)
c)
d) none of these

45) The polynomial
is exactly divisible by
if

a) m,n,k are rational
b) m,n,k are integers
c) m,n,k are positive integers
d) none of these

46) If,
then
is

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

47) The equation ,
where k is a real number, will represent a circle, if

a)
b)
c)
d)

48) If
are two nth roots of unity, then
is a multiple of

a)
b)
c)
d) none of these

49) The least positive integer n for which
is real, is

a) 2
b) 4
c) 8
d) none of these

50) Given that ‘a’ is a fixed complex number, and
is a scalar variable, the point z satisfying ztraces
out

a)
b)
c)
d) none of these

51) The equation
a) a circle of radius one unit
b) a straight line
c)
d) none of these

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

53)
a)
b)
c)
d)

54) The value of
is

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

55)
a)
b)
c)
d) none of these

56) The value of the determinant
is

a) 7+4i
b) 7-4i
c) 4+7i
d) 4-7i

57) The points representing the complex numbers z for which

a) a straight line parallel to x-axis
b) a straight line parallel to y-axis
c) a circle with centre as origin
d) a circle with centre other than the origin

58)
a)
b)
c)
d)

59)
a) x=3, y=1
b) x=1, y=3
c) x=0, y=3
d) x=0, y=0

60)
a)
b)
c)
d) none of these

61)
a) a pair of straight lines
b) a rectangular hyperbola
c) a line
d) a set of four lines

62)
a) a straight line
b) a square
c) a circle
d) none of these

63)
a) 5/7
b) 7/9
c) 25/49
d) none of these

64) The closest distance of the origin from a curve given
as

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

65)
a) equilateral triangle
b) right angled triangle
c) isosceles triangle
d) none of these

66) The roots of the cubic equation
represent the vertices of a triangle of sides of length

a)
b)
c)
d)

67)
are nth roots of vertices. The value of

a) n
b) 0
c)
d)

68) The roots of the cubic equation
a) represent vertices of an equilateral triangle
b) represent vertices of an isosceles triangle
c)
d) none of these

69) If z=x+iy, then the equation
represents a cricle when m=

a) 1/2
b) 1
c) 3
d) all the above

70)
a)
b)
c)
d)

71) Let,
is the cube root of unity, then

a)
b)
c)
d)

72) Let
be two complex numbers such that
and
both are real, then

a)
b)
c)
d)

73) Let z be a purely imaginary number such that
Then arg(z) is equal to

a)
b)
c) 0
d)

74) Let z be a purely imaginary number such that .
Then arg(z) is equal to

a)
b)
c) 0
d)

75) If z is a purely real number such that Re(z)<0, then
arg(z) is equal to

a)
b)
c) 0
d)

76) Let z be any non zero complex number. Then,
is equal to

a)
b)
c) 0
d)

77) If the complex numbers
are in AP, then they lie on a

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

78) The argument of
is

a)
b)
c)
d)

79) The smallest positive integer n for which
is

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

80) The roots of the equation
are

a)
b)
c)
d)

81) The area of the triangle formed by the complex numbers z, iz,z+iz in the argand diagram is
a)
b)
c)
d) none of these

82) Let z be a complex number. Then the angle between vectors z and iz is
a)
b) 0
c)
d) none of these

83) For any complex number
is equal to

a)
b)
c)
d) none of these

84)
a)
b)
c)
d) none of these

85) The locus of the points z satisfying the condition
a) circle
b) Y-axis
c) Parabola
d) Ellipse

86)
a)
b)
c)
d) none of these

87) The complex numbers z=x+iy which satisfy the equation
a) X-axis
b) Y-axis
c) A circle with centre (-1,0) and radius 1
d) None of these

88)
a)
b)
c)
d) none of these

89)
a) p=x, q=y
b)
c)
d) none of these

90) If z=x+iy and implies that in the complex plane
a) z lies on imaginary axis
b) z lies on real axis
c) z lies on unit circle
d) none of these

91) Let z be a complex number such that
z=

a)
b)
c)
d)

92) Let 3-i and 2+i be affixes of two points A and B in the argand plane
and P represents the complex number z=x+iy. Then the locus of P if

a) circle on AB as diameter
b) The line AB
c) The perpendicular bisector of AB
d) None of these

93) POQ is a straight line through the origin O, P and Q represent the complex numbers a+ib and c+id respectively and OP=OQ. Then
a)
b) a+c=b+d
c) arg(a+ib)=arg(c+id)
d) both a and b

94) If are complex numbers
such that , then the pair
of complex numbers satisfies

a)
b)
c)
d) all of these

95) Let be two complex
numbers such that
If has positive real
part and has negative
imaginary part, then

a) zero
b) real and positive
c) purely imaginary
d) both a and c

96) If be any two
non-zero complex such that
is equal to

a)
b)
c) 0
d)

97) The value of
a) -1
b) 0
c) -i
d) i

98) The equation where b is a non-zero complex constant and c is a real number, represents
a) a circle
b) a straight line
c) a pair of straight lines
d) none of these

99) If then the value of is
a) equal to 1
b) less than 1
c) greater than 1
d) none of these

100) If is a root of the quadratic equation then the values of a and b are respectively
a) 4, 7
b) -4, -7
c) -4, 7
d) 4, -7

Answers

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