MCQ Chapter 5 Complex Numbers and Quadratic Equations Class 11 Mathematics

Please refer to Complex Numbers and Quadratic Equations MCQ Questions Class 11 Mathematics below. These MCQ questions for Class 11 Mathematics with answers have been designed as per the latest NCERT, CBSE books and syllabus issued for the current academic year. These objective questions for Complex Numbers and Quadratic Equations will help you to prepare for the exams and get more marks.

Complex Numbers and Quadratic Equations MCQ Questions Class 11 Mathematics

Please see solved MCQ Questions for Complex Numbers and Quadratic Equations in Class 11 Mathematics. All questions and answers have been prepared by expert faculty of standard 11 based on latest examination guidelines.

MCQ Questions Class 11 Mathematics Complex Numbers and Quadratic Equations

Question: The point of intersection of the curves arg ( z – 3 i) =3π/4 and arg (2z+1- 2i )= π/4,(where i = √-1) is 
(a)1/4(3+9i)
(b)1/4(3-9i)
(c)1/2(3+2i
(d) No point 

Question:

Question: The complex number z satisfies the condition

Question:  If |z – iRe ( z)|=|z – Im ( z)| (where i = √-1), then z lies on
(a) Re (z) = 2
(b) Im (z) = 2
(c) Re (z) + Im (z) = 2
(d) None of the above 

Question: If |z₁| =|z₂ |, arg ( z₁ / z₂ ) = π, then z₁+ z₂ is equal to
(a) 0
(b) purely imaginary
(c) purely real
(d) None of these

Question: If ω is a complex cube root of unity, then the value of

Question: If z₁ and z₂ be complex numbers such that z1≠ z2  and| z₁ | |z₂ |.  If z₁ has positive real part and z₂ has negative imaginary part, then [( z₁+ z₂ )/( z₁ -z₂)] may be
(a) purely imaginary
(b) real and positive
(c) real and negative
(d) None of the above 

Question: The trigonometric form of z = (1 – i cot 8)³(where i = √-1) is

Question: If |z₁|= |z₂| =1  and amp z₁+ ampz₂= = 0, then
(a) z₁z₂ = 1
(b) z₁ + z₂ = 0
(c) z₁ =¯z2 
(d) None of these  

Question: If |z₁|< √2 – 1, then |z²+2z cos α| is
(a) less than 1
(b) 2 + 1
(c) 2 – 1
(d) None of these 

Question:

Question:  If A(z₁), B(z₂) and C(z₃)  are the vertices of the ΔABC such that ( z₁– z₂ )/( z₃ -z₂ ) = (1/√2 – (i/1/ √2 , then Δ ABC is
(a) equilateral
(b) right angled
(c) isosceles
(d) obtuse angled 

Question:

Question: The real value of q for which the expression
1+i cos θ/1-2i cos θ is a r eal num ber, is

Question: 

(a) 3 √ 3
(b)  √3
(c) 3
(d) 1/3√3

Question: If |z₁|= 15 and |z₂-3-4|5,then
(a) | z₁ – z₂ ^|_min = 5
(b) | z₁ – z₂ ^|_min = 10
(c) | z₁ – z₂ ^|_max = 20
(d) | z₁ – z₂ ^|_max = 25   

Consider the complex numbers z₁and z₂ satisfying the relation

Question: Complex number z₁¯z₂ 
(a) purely real
(b) purely imaginary
(c) zero
(d) None of these 

Question: Complex number z₁¯z₂ is
(a) purely real
(b) purely imaginary
(c) zero
(d) None of the above 

Question: One of the possible argument of complex number
i(z₁/z₂) 
(a) π/2
(b) – π/2
(c) 0
(d) None of these 

Assertion and Reason
Each of these questions contains two
statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four
alter native choices, only one of which is the correct answer. You have to select one of the codes (a), (b),(c) and (d) given be low.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true. 

Question:

Question:

Question: Consider z₁ and z₂  are two complex numbers.
Statement I Such that |z₁| |z₂ |+ |z₁– z₂ |, then Im (z₁/z₂)=0 
Statement II arg ( z) = 0⇒ z is purely real.

Question: Statement I If cos (1 – i) = a + ib, where a, b∈R and
i = √-1, then α =1/2(e+1/e) cos 1,b=1/2(e-1/e)sin 1.
Statement II e ^iθ = cos θ+i sin θ   

Question:

Question: State ment I If arg (z₁ z₂) 2π then both z₁and z₂ are purely real (z₁ and  z₂ have principal arguments).
State ment II Principal argument of complex number and between -π and π. 

Question:Statement I The product of all values of (cos α+i sin α )^3/5  is cos 3a +i sin 3a. 
State ment II The product of fifth roots of unity is 1.

Question:

Question: Statement I

is purely imaginary.

State ment II If z is purely imaginary, then z + ¯z = 0.

Question: If z is a complex number of unit modulus and argument q, then arg(1+z/1+z) is equal to
(a) -θ
(b)π/2-θ
(c) q
(d) θ – q   

Question: The number of complex numbers z such that
|z – 1|=|z + 1|=|z – i| is equal to 
(a) 0
(b) 1
(c) 2
(d) ∞   

Question: If z≠1 and z²/z-1 is real, then the point represented by the complex number z lies 
(a) either on the real axis or on a circle passing through the origin
(b) on a circle with centre at the origin
(c) either on the real axis or on a circle not passing through the origin
(d) on the imaginary axis 

Question: 

(a) √3 + 1
(b) 5 + 1
(c) 2
(d)2+√2 

Question: If |z + 4|≤ 3, then the max i mum value of |z + 1| is
(a) 4
(b) 10
(c) 6
(d) 0 

Question:

(a) 54
(b) 6
(c) 12
(d) 18 

Question: The conjugate of a complex number is 1/i – 1 . Then,that complex number is 
(a)1/i – 1
(b) -1/-1
(c)1/i + 1
(d) -1/i+ 1 

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

Question: If ω=z/z-i/3 and |ω|= 1, then z lies on
(a) a parabola
(b) a straight line
(c) a circle
(d) an ellipse

Question: If(1+i/1+i)^x=1, then
(a) x = 4n, where n is any positive integer
(b) x = 2n, where n is any positive integer
(c) x = 4n + 1, where n is any positive integer
(d) x = 2n + 1, where n is any positive integer

Question: If the cube roots of unity are 1,ω and ω² ,  then the roots of the equation (x – 1)³ + 8 = 0, are 
(a) -1,1 + 2ω,1 + 2ω²
(b) -1, 1 – 2ω,1- 2 ω²
(c) -1, -1, -1
(d) -1 -1 + 2ω-1-2ω² 

Question:

(a) 1
(b) -1
(c) 2
(d) -2

Question: If |z²-1|= |z|²+1,then z lies on
(a) the real axis
(b) the imaginary axis
(c) a circle
(d) an ellipse 

Question: Let z₁ and z₂ be two roots of the equation z²+ az+ b= 0,z being com plex. Further, assume that the origin z₁ and z₂ form an equilateral triangle. 
Then,
(a) a² =b
(b) a²  = 2b
(c) a² = 3b
(d) a² = 4b 

Question:

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

Question:

(a) 1
(b) -1
(c) i
(d) – i 

Question: Let z and w be com plex num bers such that ¯z + i¯w = 0 and arg ( zω) = π. Then, arg (z) is equal to 
(a)π /4
(b) π /2
(c) 3π /4
(d) 5π /2 

46. If ω is an imaginary cube root of unity, then
(1 ) + ω – ω²⁾⁷ is equal to 
(a) 128 w
(b) -128 w
(c) 128 w2
(d) -128 w2 

Question: If w(≠ 1) is a cube root of unity and (1+ω )⁷ = A + Bω .
Then, (A, B) is equal to
(a) (1, 1)
(b) (1, 0)
(c) (-1, 1)
(d) (0, 1) 

Question. If z=7-i/3-4i then z¹⁴ = ?     
a. 2⁷
b. 2⁷ i
c. 2¹⁴ i
d. – 2⁷i

Question. Inverse of a point a with respect to the circle |z – c| = R (a and c are complex numbers, centre C and radius R) is the point c+R2/a̅ –c̅   
a. c + R²/a̅ –c̅
b. c–R²/a̅ –c̅
c. c +R/c̅ -a̅
d. None of these

Question. If z₁ = 2+5i , z₂ = 3–i then projection of z₂ on z₂ is   
a. 1/10
b. 1 / 10
c. −7 /10
d. None of these

Question. If complex numbers z₁,z₂ and z₃ represent the vertices A, B and C respectively of an isosceles triangle ABC of which ∠C is right angle, then correct statement is   
a. z₁² + z₂² + z₃² = z₁z₂z₃
b. (z₃ – z₁)² = z₃ – z₂
c. (z₁ – z₂)² = (z₁ – z₃)(z₃ – z₂)
d. (z₁ – z₂)² = 2(z₁ – z₃)(z₃ – z₂)

Question. If zi = a + ib and z₂ = c + ib are complex numbers such that |z₁|=| z₂|=1 and 1 2 Re(z₁z₂) = 0, then the pair of complex numbers w₁ = a + ic and w₂ = b + id satisfies?   
a. |w1| = 1
b. |w2| = 1
c. 1 2 Re | w w |= 0
d. None of these

Question. Let z₁ and z₂ be complex numbers such that z₁ ≠ z₂ and |z₁|=|z₂|, If z₁ has positive real part and z2 has negative imaginary part, then z₁+z₂/z₁–z₂ may be:   
a. zero
b. real and positive
c. 0
d. 0

Question. The imaginary part of tan-1 (5i/3) is:   
a. 0
b. ∞
c. log 2
d. log 4

Question. Let ω be a complex cube root of unity with ω ≠1 and P = [p_ij] be a n×n matrix with . Pij=ω^i+j Then, P2 ≠ 0 when n is equal to:     
a. 57
b. 55
c. 58
d. 56

Question. If z₁,z₂, z₃, z₄ are the four complex numbers represented by the vertices of a quadrilateral taken in order such that z₁–z₄=z₂ –z3and amp (z₄–z₁/z₂–z₁) = π/2 , then the quadrilateral is:   
a. rhombus
b. square
c. rectangle
d. cyclic quadrilateral

Question. If z1,z2,z3,z4 are roots of the equation a₀z₄ + a₁z₃ + a₂z₂ + a₃z + a₄ = 0   
where a0, a1, a2, a3, and a4 are real, then:
a. z̅1,z̅2,z̅3,z̅4, are also roots of the equation
b. z̅1 is equal to at least one of z̅1,z̅2,z̅3,z̅4
c. –z̅1,–z̅2,–z̅3,–z̅4 are also roots of the equation d. none of the above.
d. none of the above

Assertion and Reason
Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
a. If both assertion and reason are true and the reason is the correct explanation of the assertion.
b. If both assertion and reason are true but reason is not the correct explanation of the assertion.
c. If assertion is true but reason is false.
d. If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question. Assertion: The maximum value of 

Reason: The minimum value of 

Question. Assertion: If z is a root of the equation z7 + 2x + 3 = 0, then 1 ≤ | z | < 3 / 2.     
Reason: If z lies in the annular region 1< | z | ≤ 3/ 2, then  z satisfies the 1/z-1 + 1/z-ω + 1/z-ω2 = 1 where ω ≠1 is a cube root of unity.

Question. Assertion: If ω≠1 is a cube root of unity, then A2 = O,

       
Reason: If ω≠1 is a cube root of unity, then 

Question. Assertion: If z₁, z₂ z₃ are such that |z₁| + |z₂|=|z₃|=1, then maximum value of |z₂ − z₃|² + | z₃ − z₁ | + | z₁ − z₂ | is 9.     
Reason: If z1, z₂ z₃ are such that |z₁|=|z₂|=|z₃| =1 hen Re(z₂z₃ +z₁z₂ ) ≥ 3/2.

Question. Assertion: If z² − z +1 = 0 and n is a natural number, then

denotes the greatest integer ≤ x.     
Reason: If ω ≠ 1 is a cube root of unity, then 

Question. If z1 and z2 are complex numbers, such that
|15z₁ −13z₂|² + |13z₁ +15z₂ |² = λ |z₁|² +|z₂|²), then the value of √λ√λ√λ√λ…..∞ must be equal to: