# 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**