Class 11 Mathematics Complex Numbers and Quadratic Equation MCQs

Question. If (1-i / 1+i)100 = a + ib then
(a) a = 2, b = – 1
(b) a = 1, b = 0
(c) a = 0, b = 1
(d) a = – 1, b = 2

Answer :  B
 

Question. The equation | z + 1 – i| = | z – 1 + i| represents a
(a) straight line
(b) circle
(c) parabola
(d) hyperbola

Answer :  A
 

Question. The modulus of √2i - - √2i is:
(a) 2
(b) √2
(c) 0
(d) 2√2

Answer :  A


Question. Number of solutions of the equation z2 + |z|2 = 0 is
(a) 1
(b) 2
(c) 3
(d) infinitely many

Answer :  D
 

Question. 1 + i2 + i4 + i6 + ... + i2n is
(a) positive
(b) negative
(c) 0
(d) cannot be determined

Answer :  D

Question. If f (z) = z⁴ + 9z³ + 35z² – z + 4, then the value of f (– 5 + 2 - √4 ) is:
(a) – 160
(b) 160
(c) 610
(d) 106

Answer :  A
 

Question. If z = 2 – 3i, then the value of z² – 4z + 13 is
(a) 1
(b) –1
(c) 0
(d) None of these

Answer :  C


Question. If x = 1 + i, then the value of the expression x⁴ –4x³ + 7x² – 6x + 3 is :
(a) – 1
(b) 1
(c) 2
(d) none of these

Answer :  B
 

Question. If c + i/c-i = a + ib, where a, b, c are real, then a² + b² is equal to:

(a) 7
(b) 1
(c) c²
(d) – c²

Answer :  B
 

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

Answer :  B


Question. If a ¹ b but a² = 5a – 3 and b² = 5b – 3 then the equation having a/b and b/a as its roots is
(a) 3x² – 19x + 3 = 0
(b) 3x² + 19x – 3 = 0
(c) 3x² – 19x – 3 = 0
(d) x² – 5x + 3 = 0

Answer :  A
 

Question. If x + iy = /3cos i sin 2 q + q + then 4x – x² – y² reduces to :
(a) 2
(b) 3
(c) 4
(d) 5

Answer :  B
 

Question. If (x + iy) (2 – 3i) = 4 + i, then
(a) x = – 14/13, y = 5/13
(b) x = 5/13, y = 14/13
(c) x = 14/13, y = 5/13
(d) x = 5/13, y = – 14/13

Answer :  B

Question. If | z – 4 | < | z – 2 |, its solution is given by
(a) Re(z) > 0
(b) Re(z) < 0
(c) Re(z) > 3
(d) Re(z) > 2

Answer :  C


Question. If | z + 4 | £ 3, then the maximum value of
| z + 1 | is
(a) 6
(b) 0
(c) 4
(d) 10

Answer :  A
 

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

Answer :  C
 

Question. If the conjugate of (x + iy) (1 – 2i) is 1 + i, then:
(a) y = 3/5
(b) x - iy = 1 - i /1 + 2i
(c) x + iy = 1 - i /1 - 2i
(d) x = 1/5

Answer :  C
 

Question. arg z + arg z; z ¹ 0 is equal to :
(a) π/4
(b) π
(c) 0
(d) π/2

Answer :  C
 

Question. For z = 3 - i , the principal value of arg (z) is
(a) –p/6
(b) –p/3
(c) –p/2
(d) –p/4

Answer :  A
 

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

Answer :  A
 

Question. If z1 and z2 are two non-zero complex numbers such that | z1 + z2 | = | z1 | + | z2 | , then arg z1 – arg z2 is equal to
(a) π/2
(b) – π
(c) 0
(d) -π/2

Answer :  C
 

Question. If z = x + iy satisfies 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

Answer :  B
 

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

Answer :  B
 

Question. If a + ib > c + id, then :
(a) a > c, b > d
(b) a > c, b ³ d
(c) a > c, b = d = 0
(d) none of these

Answer :  C
 

Question. The system of equations | z + 1 – i | = 2 and | z | = 3 has
(a) no solution
(b) one solution
(c) two solutions
(d) none of these

Answer :  A
 

Question. The square root of 3 + 4i is :
(a) ±{2 – i}
(b) ±{–2 + i}
(c) ±{2 + i}
(d) none of these

Answer :  C