# 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+5

*i*)

**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 circle whose radius is**

**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

**Answers**