# 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 i ^{i} 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 i ^{n} 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) i ^{57}+ 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**