Complex Numbers - Choose the correct Answers | 12th Mathematics : UNIT 2 : Complex Numbers
Chapter: 12th Mathematics : UNIT 2 : Complex Numbers
Choose the correct Answers
Choose the correct or the most suitable answer from the given four alternatives :
1. in + in+1 + in+2 + in+3 is
(1) 0
(2) 1
(3) −1
(4) i
2. The value of 
is
(1) 1+ i
(2) i
(3) 1
(4) 0
3 .The area of the triangle formed by the complex numbers z, iz, and z + iz in the Argand’s diagram is
(1) 1/2 | z |2
(2) | z |2
(3) 3/2 | z |2
(4) 2 | z |2
4. The conjugate of a complex number is 1/i-2 Then, the complex number is
(1) 1/[i+2]
(2) -1/[i+2]
(3) -1/[i-2]
(4) 1/[i-2]
5. If z= 
, then | z | is equal to
(1) 0
(2) 1
(3) 2
(4) 3
6. If z is a non zero complex number, such that 2iz2 = 
then | z | is
(1) 1/2
(2) 1
(3) 2
(4) 3
7. If | z − 2 + i | ≤ 2 , then the greatest value of | z | is
(1) √3 − 2
(2) √3 + 2
(3) √5 − 2
(4) √5 + 2
8. If 
, then the least value of | z | is
(1) 1
(2) 2
(3) 3
(4) 5
9. If | z | = 1, then the value of 
is
(1) z
(2)
(3) 1/z
(4) 1
10. The solution of the equation | z | − z = 1+ 2i is
(1) (3/2) – 2i
(2) – (3/2) + 2i
(3) 2 – (3/2)i
(4) 2 + (3/2) i
11. If | z1 | = 1, | z2 | = 2, | z3 | = 3 and | 9z1 z2 + 4z1 z3 + z2 z3 | = 12 , then the value of | z1 + z2 + z3 | is
(1) 1
(2) 2
(3) 3
(4) 4
12. If z is a complex number such that z ∈ C \ R and z + 1/z ∈ R , then | z | is
(1) 0
(2) 1
(3) 2
(4) 3
13. z1 , z3 , and z3 are complex numbers such that z1 + z2 + z3 = 0 and | z1 | =| z2 | =| z3 | = 1 then z 2 + z 2 + z 2 is
(1) 3
(2) 2
(3) 1
(4) 0
14. If (z-1) / (z+1), is purely imaginary, then | z | is
(1) 1/2
(2) 1
(3) 2
(4) 3
15. If z = x + iy is a complex number such that | z + 2 | = | z − 2 | , then the locus of z is
(1) real axis
(2) imaginary axis
(3) ellipse
(4) circle
16. The principal argument of 3/(-1+i ) is
(1) -5Ï€/6
(2) -2Ï€/3
(3) -3Ï€/4
(4) -Ï€/2
17. The principal argument of (sin 40°+ i cos 40°)5 is
(1) −110°
(2) −70°
(3) 70°
(4) 110°
18.If (1+ i) (1+ 2i) (1+ 3i)L(1+ ni) = x + iy , then 2 â‹… 5 â‹…10L(1+ n2 ) is
(1) 1
(2) i
(3) x2 + y2
(4) 1 + n2
19. If ω ≠1 is a cubic root of unity and (1+ ω)7 = A + Bω , then ( A, B) equals
(1) (1, 0)
(2) ( −1, 1)
(3) ( 0, 1)
(4) (1, 1)
20. The principal argument of the complex number 
is
(1) 2Ï€/3
(2) π/6
(3) 5Ï€/6
(4) π/2
21. If α and β are the roots of x2 + x +1 = 0 , then α 2020 + β 2020 is
(1) −2
(2) −1
(3) 1
(4) 2
22. The product of all four values of 
is
(1) −2
(2) −1
(3) 1
(4) 2
23. If ω ≠1 is a cubic root of unity and 
= 3k then k is equal to
(1) 1
(2) −1
(3) √3i
(4) − √3i
24. The value of 
is
Ans: (1)
25.If ω = cis (2π/3), then the number of distinct roots of 
(1) 1
(2) 2
(3) 3
(4) 4
Choose the correct or the most suitable answer from the given four alternatives :
1. in + in+1 + in+2 + in+3 is
(1) 0
(2) 1
(3) −1
(4) i
2. The value of is
(1) 1+ i
(2) i
(3) 1
(4) 0
3 .The area of the triangle formed by the complex numbers z, iz, and z + iz in the Argand’s diagram is
(1) 1/2 | z |2
(2) | z |2
(3) 3/2 | z |2
(4) 2 | z |2
4. The conjugate of a complex number is 1/i-2 Then, the complex number is
(1) 1/[i+2]
(2) -1/[i+2]
(3) -1/[i-2]
(4) 1/[i-2]
5. If z= , then | z | is equal to
(1) 0
(2) 1
(3) 2
(4) 3
6. If z is a non zero complex number, such that 2iz2 = then | z | is
(1) 1/2
(2) 1
(3) 2
(4) 3
7. If | z − 2 + i | ≤ 2 , then the greatest value of | z | is
(1) √3 − 2
(2) √3 + 2
(3) √5 − 2
(4) √5 + 2
8. If , then the least value of | z | is
(1) 1
(2) 2
(3) 3
(4) 5
9. If | z | = 1, then the value of is
(1) z
(2)
(3) 1/z
(4) 1
10. The solution of the equation | z | − z = 1+ 2i is
(1) (3/2) – 2i
(2) – (3/2) + 2i
(3) 2 – (3/2)i
(4) 2 + (3/2) i
11. If | z1 | = 1, | z2 | = 2, | z3 | = 3 and | 9z1 z2 + 4z1 z3 + z2 z3 | = 12 , then the value of | z1 + z2 + z3 | is
(1) 1
(2) 2
(3) 3
(4) 4
12. If z is a complex number such that z ∈ C \ R and z + 1/z ∈ R , then | z | is
(1) 0
(2) 1
(3) 2
(4) 3
13. z1 , z3 , and z3 are complex numbers such that z1 + z2 + z3 = 0 and | z1 | =| z2 | =| z3 | = 1 then z 2 + z 2 + z 2 is
(1) 3
(2) 2
(3) 1
(4) 0
14. If (z-1) / (z+1), is purely imaginary, then | z | is
(1) 1/2
(2) 1
(3) 2
(4) 3
15. If z = x + iy is a complex number such that | z + 2 | = | z − 2 | , then the locus of z is
(1) real axis
(2) imaginary axis
(3) ellipse
(4) circle
16. The principal argument of 3/(-1+i ) is
(1) -5Ï€/6
(2) -2Ï€/3
(3) -3Ï€/4
(4) -Ï€/2
17. The principal argument of (sin 40°+ i cos 40°)5 is
(1) −110°
(2) −70°
(3) 70°
(4) 110°
18.If (1+ i) (1+ 2i) (1+ 3i)L(1+ ni) = x + iy , then 2 â‹… 5 â‹…10L(1+ n2 ) is
(1) 1
(2) i
(3) x2 + y2
(4) 1 + n2
19. If ω ≠1 is a cubic root of unity and (1+ ω)7 = A + Bω , then ( A, B) equals
(1) (1, 0)
(2) ( −1, 1)
(3) ( 0, 1)
(4) (1, 1)
20. The principal argument of the complex number is
(1) 2Ï€/3
(2) π/6
(3) 5Ï€/6
(4) π/2
21. If α and β are the roots of x2 + x +1 = 0 , then α 2020 + β 2020 is
(1) −2
(2) −1
(3) 1
(4) 2
22. The product of all four values of is
(1) −2
(2) −1
(3) 1
(4) 2
23. If ω ≠1 is a cubic root of unity and = 3k then k is equal to
(1) 1
(2) −1
(3) √3i
(4) − √3i
24. The value of is
Ans: (1)
25.If ω = cis (2π/3), then the number of distinct roots of
(1) 1
(2) 2
(3) 3
(4) 4
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