Class 11 Mathematics Complex Numbers and Quadratic Equation MCQs Set 03

Question: The maximum distance from the origin of coordinates to the point z satisfying the equation

Answer: c

Question:

a) (0, – 2)
b) (-2, 0)
c) (0, 2)
d) (2, 0)
Answer: c

Question: Let z₁,z₂ and z₃ be the affixes of the vertices of a triangle having the circumcenter at the origin. If z is the affix of it’s orthocenter then z is equal to
a) z₁+ z₂+ z₃ 
b) z₁+ z₂+ z₃/2
c) z₁+ z₂+ z₃ 
d) None of the options
Answer: c

Question:

Answer: b

Question:

a) 8
b) 10
c) 12
d) None of the options
Answer: a

Question: The num ber of non-zero in te gral so lu tions of the equa tion |1 – i|x = 2x is
a) infinite
b) 1
c) 2
d) None of the options
Answer: b

Question:

Answer: d

Question: If the comp lex num bers iz, z and z + iz rep re sent the three ver ti ces of a triangle, then the area of the triangle is

Answer: b

Question: If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 200, then the value of |3 z| must be equal to
a) 20
b) 40
c) 60
d) 80
Answer: c

Question: Given that the equation z²+(p+iq) z+ r+ is =0 where p, q, rand s are real and non-zero roots, then
a) pqr = r² + p²s
b) prs = q² + r²p
c) qrs = p² + s²q
d) pqs = s² + q²r
Answer: d

Question: If iz³+ z²– z +i =0,then |z| is equal to
a) 1
b) i
c) -1
d) – i
Answer: a

Question: In a given parallelogram, if the points P₁ and P₂ represent two complex numbers z₁ and z₂,then the point P₃ represents the num ber
a) z₁+ z₂
b) z₁– z₂
c) z₁x z₂
d) z₁÷ z₂
Answer: a

Question: The points rep re sented by the com plex num bers 1 + i, -2 +3 i and 5/3 i on the ar gand di a gram are
a) vertices of an equilateral triangle
b) vertices of an isosceles triangle
c) collinear
d) None of the options
Answer: c

Question: If w( ¹ 1) is a cube root of unity and (1 ) , + w 7 = A + Bw then A and B are re spec tively
a) 0 , 1
b) 1, 1
c) 1, 0
d) -1, 1
Answer: b

Question: If w is a com plex cube root of unity, then for pos i tive in te gral value of n, the prod uct of w× w2 × w3 w ….. n will be
a) 1-i√3/2
b) 1-I√3/2
c) 1
d) Both 1-I√3/2 and 1
Answer: b

Question:

Answer: b

Question: If Im (z-1/2z+1) = -4, then lo cus of z is
a) an ellipse
b) a parabola
c) a straight line
d) a circle
Answer: d

Question:

Answer: a

Question: If the real part of

is 4, then the locus of the point representing z in the complex plane is
a) a circle
b) a parabola
c) a hyperbola
d) an ellipse
Answer: a

Question: In a given parallelogram, if the points P₁ and P₂ represent two complex numbers z₁ and z₂,then the point P₃ represents the number

a) z₁ + z₂
b) z₁ – z₂
c) z₁ x z₂
d) z₁ + z₂
Answer: a

Question:|z₁+z₂ |=|z₁ |+|z₂| is possible, if
a) z₂ ¯z₁=
b) z₂ =1/z₁
c) arg (z₁) = arg (z₂)
d) | z₁ | | z₂ |
Answer: c

Question: If| z – 2|= min {|z – 1|,|z – 5|} , where z is a complex number, then
a) Re (z) = 3/2
b) Re (z) = 7/2
c) Re (z ) ∈{3/2,7/2}
d) None of the options
Answer: c

Question: Locus of z, if arg (z-1/z+1) = π/2 , is
a) a circle
b) a semi-circle
c) a straight line
d) None of the options
Answer: b

Question: Let z be a complex number and a be a real parameter such that z₂ + ax + a₂ = 0, then
a) locus of z is a pair of straight lines
b) locus of z is a circle
c) arg (z) = ± 5π/3
d) |z | = – 2|a |
Answer: a

Question:

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

Question: The points rep re sented by the com plex num bers 1 + i, -2 + 3i and 5/3 on the ar gand di a gram are
a) vertices of an equilateral triangle
b) vertices of an isosceles triangle
c) collinear
d) None of the options
Answer: c

Question: If x = a + b, y = aa + bb and z = ab + ba, where a and b are complex cube roots of unity, then xyz is equal to
a) a² + b²
b) a³ + b³
c) a³b³
d) a³ – b³
Answer: b

Question: Let z₁ and z₂ be the non-real roots of the equa tion 3z2 + 3z + b = . If the ori gin to gether with thepoints rep re sented by z₁ and z₂ and form an equi lat eral tri an gle, then the value of b is
a) 1
b) 2
c) 3
d) None of the options
Answer: a

Question: The area of the tri an gle whose ver ti ces are rep re sented by the com plex num bers 0, z zei , a,(0 < a < p) is equal to
a) 1/2|z|²cosα
b) 1/2|z|² sinα
c) 1/2|z|² sinαcosα
d) 1/2||z|²
Answer: d

Question: The lo cus of the points z which sat isfy the con di tion arg (z-1/z+1) = π/3 , is
a) a straight line
b) a circle
c) a parabola
d) None of the options
Answer: b

Question: If z and w are two non-zero com plex num bers such that |zw|= 1 and arg ( z) – arg (w) = , π/2 then z̄w is equal to
a) 1
b) -1
c) i
d) – i
Answer: d

Question: If the real part of z̄+2/z̄-1 is 4, then the lo cus of the point representing z in the com plex plane is
a) a circle
b) a parabola
c) a hyperbola
d) an ellipse
Answer: a

Question: In the ar gand plane the com plex num ber z = 4 – 3 i is turned in the clock wise sense through 180° and stretched three times. The com plex num ber rep re sented by the new num ber is
a) 12 + 9i
b) 12 – 9i
c) -12 – 9i
d) -12 + 9i
Answer: d

Question: The equa tion of a cir cle whose ra dius and centre are r and z0 respectively, is
a) zz̄ – zz̄₀ – z̄z₀ + z₀z̄₀ = r²
b) zz̄ + zz̄₀ – z̄z₀ + z₀z̄₀ = r²
c) zz̄ – zz̄₀ + z̄z₀ – z₀z̄₀ = r²
d) None of the options
Answer: a

Question: If z₁ and z₂ are two non-zero com plex num bers such that |z₁ + z₂| = |z₂| |z₁| + |z₂| then arg ( z₂ ) arg is equal to
a) -π/2
b) 0
c) -π
d) π/2
Answer: b

Question:

Answer: a

Question:|z-2/z+2| =π/6 , then the lo cus of z is
a) a straight line
b) a circle
c) a parabola
d) an ellipse
Answer: b