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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, Multiple choice questions with Answers, Solution - Maths Book back 1 mark questions and answers with solution for Exercise Problems

Choose the correct or the most suitable answer from the given four alternatives :

 

1. i+ in++ in++ in+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 ziz, and + 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 | | is equal to

(1) 0

(2) 1

(3) 2

(4) 3


 

6. If is a non zero complex number, such that 2iz=  then | | is

(1) 1/2

(2) 1

(3) 2

(4) 3


 

7. If |  2 +  2 , then the greatest value of | | is

(1) √3 − 2

(2) √3 + 2

(3) √5 − 2 

(4) √5 + 2


 

8. If , then the least value of | | is

(1) 1

(2) 2

(3) 3

(4) 5


 

9. If | = 1, then the value of  is

(1) z

(2) 

(3) 1/z

(4) 1


 

10. The solution of the equation | − = 1+ 2is

(1) (3/2) – 2i

(2) –  (3/2) + 2i 

(3) 2 – (3/2)i 

(4) 2 + (3/2) i 


 

11. If | z= 1, | z= 2, | z= 3 and | 9zz+ 4zz+ zz= 12 , then the value of | z+ z+ z| is

(1) 1

(2) 2

(3) 3

(4) 4


 

12. If is a complex number such that  R and + 1/z  R , then | | is

(1) 0

(2) 1

(3) 2

(4) 3


 

13. zz, and zare complex numbers such that z+ z+ z= 0 and | z=z=z= 1 then + + is

(1) 3

(2) 2

(3) 1

(4) 0


 

14. If (z-1) / (z+1), is purely imaginary, then | | is

(1) 1/2

(2) 1

(3) 2

(4) 3


 

15. If = + iy is a complex number such that | + 2 | = |  2 | , then the locus of is

(1) real axis

(2) imaginary axis

(3) ellipse

(4) circle


 

16. The principal argument of 3/(-1+i ) is

(1) -5π/6

(2) -2π/3

(3) -3π/4

(4) -π/2


 

17. The principal argument of (sin 40°+ cos 40°)5  is

(1) −110°

(2) −70°

(3) 70°

(4) 110°


 

18.If (1+ i) (1+ 2i) (1+ 3i)L(1+ ni= + iy , then 2  5 10L(1+ n) is

(1) 1

(2) i

(3) x2 + y2

(4) 1 + n2


 

19. If ω  1 is a cubic root of unity and (1+ ω)= + Bω , then ( AB) equals

(1) (1, 0)

(2) ( −1, 1)

(3) ( 0, 1)

(4) (1, 1)


 

20. The principal argument of the complex number  is

(1) 2π/3

(2) π/6

(3) 5π/6

(4) π/2


 

21. If α and β are the roots of x+ += 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 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. i+ in++ in++ in+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 ziz, and + 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 | | is equal to

(1) 0

(2) 1

(3) 2

(4) 3

 

6. If is a non zero complex number, such that 2iz=  then | | is

(1) 1/2

(2) 1

(3) 2

(4) 3

 

7. If |  2 +  2 , then the greatest value of | | is

(1) √3 − 2

(2) √3 + 2

(3) √5 − 2 

(4) √5 + 2

 

8. If , then the least value of | | is

(1) 1

(2) 2

(3) 3

(4) 5

 

9. If | = 1, then the value of  is

(1) z

(2) 

(3) 1/z

(4) 1

 

10. The solution of the equation | − = 1+ 2is

(1) (3/2) – 2i

(2) –  (3/2) + 2i 

(3) 2 – (3/2)i 

(4) 2 + (3/2) i 

 

11. If | z= 1, | z= 2, | z= 3 and | 9zz+ 4zz+ zz= 12 , then the value of | z+ z+ z| is

(1) 1

(2) 2

(3) 3

(4) 4

 

12. If is a complex number such that  R and + 1/z  R , then | | is

(1) 0

(2) 1

(3) 2

(4) 3

 

13. zz, and zare complex numbers such that z+ z+ z= 0 and | z=z=z= 1 then + + is

(1) 3

(2) 2

(3) 1

(4) 0

 

14. If (z-1) / (z+1), is purely imaginary, then | | is

(1) 1/2

(2) 1

(3) 2

(4) 3

 

15. If = + iy is a complex number such that | + 2 | = |  2 | , then the locus of is

(1) real axis

(2) imaginary axis

(3) ellipse

(4) circle

 

16. The principal argument of 3/(-1+i ) is

(1) -5π/6

(2) -2π/3

(3) -3π/4

(4) -π/2

 

17. The principal argument of (sin 40°+ cos 40°)5  is

(1) −110°

(2) −70°

(3) 70°

(4) 110°

 

18.If (1+ i) (1+ 2i) (1+ 3i)L(1+ ni= + iy , then 2  5 10L(1+ n) is

(1) 1

(2) i

(3) x2 + y2

(4) 1 + n2

 

19. If ω  1 is a cubic root of unity and (1+ ω)= + Bω , then ( AB) equals

(1) (1, 0)

(2) ( −1, 1)

(3) ( 0, 1)

(4) (1, 1)

 

20. The principal argument of the complex number  is

(1) 2π/3

(2) π/6

(3) 5π/6

(4) π/2

 

21. If α and β are the roots of x+ += 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 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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12th Mathematics : UNIT 2 : Complex Numbers


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