# Assignments Class 11 Mathematics Complex Numbers and Quadratic Equations

Please refer to Assignments Class 11 Mathematics Complex Numbers and Quadratic Equations Chapter 5 with solved questions and answers. We have provided Class 11 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 5 Complex Numbers and Quadratic Equations Class 11 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

## Complex Numbers and Quadratic Equations Assignments Class 11 Mathematics

Question. If z = a + ib, then real and imaginary part of z are
(a) Re(z) = a, Im(z) = b
(b) Re(z) = b, Im(z) = a
(c) Re(z) = a, Im(z) = ib
(d) None of these

A

Question. The conjugate of the complex number 2+5i/4–3i is equal to :
(a) 7– 26i/25
(b) –7– 26i/25
(c) – 7+26i/25
(d) 7+26i/25

C

Question. The solution of √3x2 – 2 = 2x –1 are :
(a) (2, 4)
(b) (1, 4)
(c) (3, 4)
(d) (1, 3)

D

Question. If z = x –i y and z3 = p + iq, then (x/p + y/q) / (p2 + q2) is equal to
(a) –2
(b) –1
(c) 2
(d) 1

A

Question. Simplify the complex numbers given in column-I and match with column-II.

Codes:
A B C
(a) 1 2 3
(b) 2 1 3
(c) 1 3 2
(d) 2 3 1

B

Question. If one root of ax2 + bx + c = 0 be square of the other, then the value of b3 + ac2 + a2 c is
(a) 3abc
(b) –3abc
(c) 0
(d) None of these

A

Question. The value of

(a) 1 – √2
(b) 1 + √2
(c) 1 ± √2
(d) None of these

B

Question. If z is a complex number such that z – 1/z + 1 is purely imaginary, then
(a) |z | = 0
(b) |z | = 1
(c) |z | > 1
(d) |z | < 1

B

Question. Find the value of a such that the sum of the squares of the roots of the equation x2 – (a – 2)x – (a + 1) = 0 is least.
(a) 4
(b) 2
(c) 1
(d) 3

C

Question. If z1 = 2 + 3i and z2 = 3 – 2i, then z1 – z2 equals to –1 + bi. The value of ‘b’ is
(a) 1
(b) 2
(c) 3
(d) 5

D

Question. If z is a complex number such that z2 = (z̄)2 , then
(a) z is purely real
(b) z is purely imaginary
(c) either z is purely real or purely imaginary
(d) None of these

C

Question. Simplify the complex numbers given in column-I and match with column-II

Codes:
A B C D
(a) 1 2 3 4
(b) 2 1 3 4
(c) 2 3 4 1
(d) 1 4 3 2

B

Question. The roots of the given equation (p – q) x2 + (q – r) x + (r – p) = 0 are :
(a) p–q/r–p,1
(b) q–r/p–q,1
(c) r–p/p–q,1
(d) None of these

C

Question. If x = √–16, then
(a) x = 4i
(b) x = 4
(c) x = – 4
(d) All of these

A

Question. If (x + iy)1/3 = a + ib, where x, y, a, b ∈ R, then x/a – y/b =
(a) a2 – b2
(b) –2(a2 + b2)
(c) 2(a2 – b2)
(d) a2 + b

B

Question. Product of real roots of the equation t2x2+|x|+9 = 0
(a) is always positive
(b) is always negative
(c) does not exist
(d) None of these

A

Question. The value of (1 + i)(1 + 1/1)is
(a) 12
(b) 2
(c) 8
(d) 16

D

Question. If α, β be the roots of the equation 2x2 – 35x + 2 = 0, then the value of (2α – 35)3 . (2β – 35)3 is equal to
(a) 1
(b) 64
(c) 8
(d) None of these

B

Question. The roots of equation x–2/x–1 = 1– 2/x–1 is
(a) one
(b) two
(c) infinite
(d) None of these

B

Question. The solutions of the quadratic equation ax2 + bx + c = 0, where a, b, c ∈ R, a ≠ 0, b2 – 4ac < 0, are given by x = ?

C

Question. Solve √5x2 + x + √5 = 0.
(a) ± √19/5 i
(b) ± √19i/2
(c) – 1± √19i/2√5
(d)  – 1± √19i/√5

C

Question. If the roots of the equation x2 – 5x + 16 = 0 are α, β and the roots of equation x2 + px + q = 0 are α2 + β2, αβ/2 ,then
(a) p = 1, q = –56
(b) p = –1, q = –56
(c) p = 1, q = 56
(d) p = –1, q = 56

B

Question. Evaluate: (1 + i)6 + (1 – i)3.
(a) –2 – 10i
(b) 2 – 10i
(c) –2 + 10i
(d) 2 + 10i

A

Question. If z1 = √3 + i√3 and z2 = √3 + i , then in which quadrant z1/zlies?
(a) I
(b) II
(c) III
(d) IV

A

Question. Value of (2i/1+i)is
(a) i
(b) 2i
(c) 1 – i
(d) 1 – 2i

B

Question. If z(2 – i) = (3 + i), then z20 is equal to
(a) 210
(b) –210
(c) 220
(d) –220

B

Question. If z1 = 3 + i and z2 = i – 1, then
(a) | z1 + z2| > |z1| + |z2|
(b) | z1+ z2 | < |z1| – |z2|
(c) |z1 + z2| ≤ |z1| + |z2|
(d) |z1 + z2| < |z1| + |z2|

D

Question. Simplify the complex numbers given in column-I and match with column-II

Codes:
A B C D E
(a) 5 4 3 2 1
(b) 4 1 5 2 3
(c) 4 2 5 1 3
(d) 3 1 2 5 4

B

Question. Let z be any complex number such that | z | = 4 and arg (z) = 5π/6 , then value of z is
(a) –2√3 – 2i
(b) 2√3 – i
(c) √2 + 3i
(d) –2√3 + 2i

D

Question. If α, β are the roots of the equation ax2 + bx + c = 0, then the value of 1/aα + b + 1/aβ + b equals
(a) ac/b
(b) 1
(c) ab/c
(d) b/ac

D

Question. If x2 + y2 = 25, xy = 12, then x =
(a) {3, 4}
(b) {3, –3}
(c) {3, 4, –3, –4}
(d) {–3, –3}

C

Question. If x2 + ax + 10 = 0 and x2 + bx – 10 = 0 have a common root, then a2 – b2 is equal to
(a) 10
(b) 20
(c) 30
(d) 40

C

Question. i57 + 1 /i25  when simplified has the value
(a) 0
(b) 2i
(c) – 2i
(d) 2

A

Question. The modulus of (1 + i√3)(2 +2i)/(√3–i) is
(a) 2
(b) 4
(c) 3√2
(d) 2√2

D

Question. If the product of the roots of the equation (a + 1)x2 + (2a + 3)x + (3a + 4) = 0 be 2, then the sum of roots is
(a) 1
(b) –1
(c) 2
(d) –2

A

Question. Modulus of z = (1 + i√3)(cosθ+ isinθ)/2(1 – i)(cosθ– isinθ)  is
(a) 1/√3
(b) – 1/√2
(c) 1/√2
(d) 1

C

Question. The argument of the complex number (i/2 – 2/i) is equal to
(a) π/4
(b) 3π/4
(c) π/12
(d) π/2

D

Question. Value of k such that equations 2x2 + kx – 5 = 0 and x2 – 3x – 4 = 0 have one common root, is
(a) –1, –2
(b) –3, –27/4
(c) 3, 4/27
(d) –2, – 3

B

Question. √–3 √–6 is equal to
(a) 3√2
(b) –3√2
(c) 3√2 i
(d) –3√2i

B

Question. If the complex numbers z1, z2,z3 represents the vertices of an equilateral triangle such that | z1 | = | z2 | = | z3 |, then value of z1 + z2 + z3 is
(a) 0
(b) 1
(c) 2
(d) 3/2

A

Question. If α and β are the roots of the equation x2 + 2x + 4 = 0, then 1/α3 + 1/βis equal to
(a) – 1/2
(b) 1/2
(c) 32
(d) 1/4

D

Question. Amplitude of 1+√3i/√3+1 is :
(a) π/6
(b) π/4
(c) π/3
(d) π/2

C

Question. If the sum of the roots of the equation x2 + px + q = 0 is three times their difference, then which one of the following is true?
(a) 9p2 = 2q
(b) 2q2 = 9p
(c) 2p2 = 9q
(d) 9q2 = 2p

C

Question. If a < b < c < d, then the nature of roots of ( x – a) (x – c) + 2 (x – b) (x – d) = 0 is
(a) real and equal
(b) complex
(c) real and unequal
(d) None of these

C

Question. Which of the following is correct for any two complex numbers z1 and z2?
(a) |z1 z2| = |z1| |z2|
(b) arg(z1 z2) = arg(z1) . arg(z2)
(c) |z1 + z2| = |z1| + |z2|
(d) |z1 + z2| ≥ |z1| – |z2

A

Question. The value of (1 + i)5 (1 – i)5 is 2n. ‘n’ is equal to
(a) 2
(b) 3
(c) 4
(d) 5

D

Question. The complex number 1+ 2i/1–i lies in:

B

Question. For the equation 1/x + a – 1/x + b = 1/x + c , if the product of roots is zero, then sum of roots is
(a)– 2bc/b+c
(b) 2ca/c + a
(c) bc/c + a
(d) –bc/b+c

A

Question. Represent z = 1 + i √3 in the polar form.
(a) cosπ/3 + i sinπ/3
(b) cosπ/3 – i sinπ/3
(c) 2 (cosπ/3 + i sinπ/3)
(d) 4 cosπ/3 + i sinπ/3)

C

Question. If z1 = 2 – i and z2 = 1 + i, then value of |z1 + z2 + 1/z1 – z2 + 1| is
(a) 2
(b) 2i
(c) 2
(d) 2i

C

Question. If z1 = 2 + 3i and z2 = 3 + 2i, then z1 + z2 equals to a + ai. Value of ‘a’ is equal to
(a) 3
(b) 4
(c) 5
(d) 2

C

Question. If the sum of the roots of the equation x2 + px + q = 0 is equal to the sum of their squares, then
(a) p2 – q2 = 0
(b) p2 + q2 = 2q
(c) p2 + p = 2q
(d) None of these

C

Question. The value of (1 + i)8 + (1 – i)8 is 2n. Value of n is
(a) 2
(b) 3
(c) 4
(d) 5

D

Question. If ax2 + bx + c = 0 is a quadratic equation, then equation has no real roots, if
(a) D > 0
(b) D = 0
(c) D < 0
(d) None of these

C

Question. If z be the conjugate of the complex number z, then which of the following relations is false?
(a) |z| =| z̄|
(b) z.z̄ = | z̄|2
(c)  z̄1 + z̄2 = z̄1 + z̄2
(d) arg z = arg z̄

D

Question. Additive inverse of 1 – i is
(a) 0 + 0i
(b) –1 – i
(c) –1 + i
(d) None of these

C

Question. The roots of the equation 32x – 10.3x + 9 = 0 are
(a) 1, 2
(b) 0, 2
(c) 0, 1
(d) 1, 3

B

Question. If 2 + i√3 is a root of the equation x2 + px + q = 0, where p and q are real, then (p, q) =
(a) (–4, 7)
(b) (4, –7)
(c) (4, 7)
(d) (–4, –7)

A

Question. If x2 + x + 1 = 0, then what is the value of x ?
(a) 1 + √3i/2
(b) –1 ± √3i/2
(c) –1 ± √3i/3
(d) –1 ± √2i/2