# Class 11 Mathematics Chapter 5 Complex Numbers and Quadratic Equations MCQ Questions with Answer

Complex Numbers and Quadratic Equations Class 11 MCQ is one of the best strategies to prepare for the CBSE Class 11 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more Complex Numbers and Quadratic Equations class 11 MCQ which will help them all through their board test.

## Complex Numbers and Quadratic Equations Class 11 MCQ Questions with Answer

Class 11 Math MCQ with answers are given here to Chapter 5 Complex Numbers and Quadratic Equations. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 11 Mathematics syllabus. By Solving these Class 11 MCQs, you will be able to analyze all of the concepts quickly in the Chapter and get ready for the Class 11 Annual exam.

Learn Complex Numbers and Quadratic Equations Class 11 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 11 Complex Numbers and Quadratic Equations MCQ with answers given below.

Question 1. 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 (b) and (c)

B

Question 2. Com mon roots of the equa tions z3+z2 + 2z + 1 = 0 and  z1985 + z100 = 0 are
(a) ω, ω2
(b) ω, ω3
(c) ω2 ω3 ,
(d) None of these

B

Question 3. If a1 , a2 , …, an -1 are n roots of unity, then the value of (1- a1 ) (1- a2) (1- a3) . . . (1- an-1) is equal to
(a) 3
(b) 1/2
(c) n
(d) 0

C

Question 4. 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

D

Question 5. The val ues of ( ) / 16 1 4 are
(a) ±2, ± 2 i
(b) ±4 , ± 4 i
(c) ±1, ± i
(d) None of these

A

Question 6. If x = a + b, y = aa + bb and z = ab + ba, where a and b are com plex cube roots of unity, then xyz is equal to
(a) a2 + b2
(b) a3 + b3
(c) a3b3
(d) a3 – b3

B

Question 7. 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

B

Question 8. 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 these

B

Question 9. 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 these

B

Question 10. 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 |

A

Question 11. 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

D

Question 12. If the com plex num bers z z 1 2 and and the or i gin form an equi lat eral tri an gle, then z12 + z22 is equal to
(a) z1z2
(b) z1z2
(c) z2z1
(d) |z1|2 = |z2|2

A

Question 13. In a given par al lel o gram, if the points P1 and P2 represent two com plex num bers z1 and z2,then the point P3 represents the num ber
(a) z1 + z2
(b) z1 – z
(c) z1 x z2
(d) z1 + z2

A

Question 14. 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 these

A

Question 15. 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

C

Whoever needs to take the CBSE Class 11 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 11 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Complex Numbers and Quadratic Equations Class 11 MCQ are ready by the subject specialists themselves.

Question 16. Re( z ) 2 = 1 is rep re sented by
(a) the circle x2 + y2  = 1
(b) the hyperbola x2 – y2 = 1
(c) parabola or a circle
(d) All of these

B

Question 17. If the comp lex num bers iz, z and z + iz rep re sent the three ver ti ces of a tri an gle, then the area of the tri an gle is
(a) 1/2|z|2
(b) |z|2
(c) 1/2|z – 1|
(d) |z – 1|2

A

Question 18. If z1 , z2 , z3  and z4 are the af fixes of four points in the ar gand plane and z is the af fix of a point, such that
|z – z1|=|z – z2|=|z – z3|=|z – z4|, then and are
(a) concyclic
(b) vertices of a parallelogram
(c) vertices of a rhombus
(d) in a straight line

A

Question 19. Let z and ω be com plex num bers such that z + iw = 0 and arg ( zω) = p. Then, arg (z̄) is equal to
(a) π /4
(b) π /2
(c) 3π /4
(d) 5π /2

C

Question 20. If |z2 – | |z|2 + 1 = + 1 then z lies on
(a) the real axis
(b) the imaginary axis
(c) a circle
(d) an ellipse

B

Question 21. 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 above

C

Question 22. 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

D

Question 23. 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

A

Question 24. The equa tion of a cir cle whose ra dius and centre are r and z0 respectively, is
(a) zz̄ – zz̄0 – z̄z0 + z00 = r2
(b) zz̄ + zz̄0 – z̄z0 + z00 = r2
(c) zz̄ – zz̄0 + z̄z0 – z00 = r2
(d) None of the above

A

Question 25. 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|2 cosα
(b) 1/2|z|2 sinα
(c) 1/2|z|2 sinαcosα
(d) 1/2|z|2

D

Question 26. If z3 + z2 – z + i = 0, then |z| is equal to
(a) 1
(b) i
(c) -1
(d) – i

A

Question 27. The centre of the circle
zz̄ – (2 + 3i) z – (2 – 3i)z̄ + 9 = 0 is
(a) (2, – 3)
(b) (2, 3)
(c) (-2, – 3)
(d) (-2, 3)

A

Question 28. 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 these

B

Question 29.|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

B

Question 30. 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

B

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