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Complex Numbers Quiz for TGT, PGT, NDA, KVS, PCS, LT Grade, ETCE

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Complex Numbers Quiz (50 Questions)

Complex Numbers Quiz for TGT, PGT, NDA, KVS, PCS, LT Grade, ETCE

1. What is the modulus of the complex number z = 3 + 4i? (KVS PGT 2018)

a) 3 b) 5 c) 7 d) 25

2. What is the conjugate of z = 2 – 3i? (NDA 2019)

a) -2 + 3i b) 2 – 3i c) 2 + 3i d) -2 – 3i

3. If z = 1 + i, what is z²? (UP TGT 2021)

a) 2 b) 2i c) -2 d) -2i

4. What is the argument of z = -1 + i? (KVS TGT 2018)

a) π/4 b) 3π/4 c) π/2 d) -π/4

5. Express z = √3 + i in polar form. (NDA 2020)

a) 2(cos(π/3) + i sin(π/3)) b) √2(cos(π/6) + i sin(π/6)) c) 2(cos(π/6) + i sin(π/6)) d) 2(cos(π/4) + i sin(π/4))

6. If z = 2 + 3i, what is |z|²? (PCS 2019)

a) 5 b) 7 c) 13 d) 9

7. Find the real part of (1 + i)/(1 – i). (LT Grade 2020)

a) 1 b) 0 c) -1 d) 2

8. What is the cube of z = i using De Moivre’s theorem? (NDA 2021)

a) 1 b) i c) -i d) -1

9. If z₁ = 2 + i, z₂ = 1 + 2i, find z₁z₂. (KVS PGT 2020)

a) 2 + 5i b) 5i c) 3 + 5i d) 5 + i

10. Find the square roots of i. (UP PGT 2022)

a) ±(1 + i) b) ±(1/√2 – i/√2) c) ±(1/√2 + i/√2) d) ±i

11. If z = 3 – 4i, find 1/z. (KVS PGT 2019)

a) 3/25 + 4i/25 b) 3/25 – 4i/25 c) -3/25 + 4i/25 d) 4/25 – 3i/25

12. What is the modulus of z = -√2 + i√2? (NDA 2022)

a) 2 b) √2 c) 2√2 d) 1

13. If z = cos(π/3) + i sin(π/3), find z³. (UP TGT 2020)

a) 1 b) -1 c) i d) -i

14. Find the imaginary part of (2 + i)/(2 – i). (PCS 2021)

a) 1/5 b) 3/5 c) -1/5 d) 0

15. If |z| = 3 and arg(z) = π/4, what is z? (LT Grade 2021)

a) 3(1 + i)/√2 b) 3(1 – i)/√2 c) 3(i + 1) d) 3(i – 1)

16. What is the sum of z = 5 + 2i and its conjugate? (KVS TGT 2019)

a) 5 b) 10 c) 4i d) 0

17. Find the modulus of z = -3 – 3i. (NDA 2018)

a) 3 b) 6 c) 3√2 d) √3

18. What is the argument of z = -1 – i? (UP PGT 2019)

a) -π/4 b) -3π/4 c) π/4 d) 3π/4

19. If z = 2i, find z⁴. (KVS PGT 2021)

a) -16 b) -16i c) 16 d) 16i

20. Express z = 1 – i in polar form. (NDA 2020)

a) √2(cos(π/4) + i sin(π/4)) b) √2(cos(-π/4) + i sin(-π/4)) c) 2(cos(π/4) + i sin(π/4)) d) √2(cos(π/2) + i sin(π/2))

21. If z₁ = 1 + i, z₂ = 1 – i, find |z₁ + z₂|. (PCS 2020)

a) √2 b) 4 c) 2 d) 2√2

22. What is the real part of z = (3 + 2i)²? (LT Grade 2019)

a) 9 b) 5 c) 12 d) -4

23. Find the cube roots of 1. (KVS PGT 2022)

a) 1, -1, i b) 1, i, -i c) 1, (-1 + i√3)/2, (-1 – i√3)/2 d) 1, 1 + i, 1 – i

24. If z = 2 + i, find z̅/z. (NDA 2021)

a) (4 + i)/5 b) (4 – i)/5 c) 1 d) (2 – i)/5

25. What is the polar form of z = -2? (UP TGT 2022)

a) 2(cos(0) + i sin(0)) b) 2(cos(π) + i sin(π)) c) 2(cos(π/2) + i sin(π/2)) d) 2(cos(-π/2) + i sin(-π/2))

26. If z = 1 + i√3, find |z|². (KVS TGT 2020)

a) 2 b) 3 c) 4 d) 6

27. Find the imaginary part of (1 – i)³. (PCS 2018)

a) -2 b) 2 c) 0 d) 3

28. If z = cos(π/6) + i sin(π/6), find z⁵. (NDA 2022)

a) cos(π/3) + i sin(π/3) b) cos(π/6) + i sin(π/6) c) cos(5π/6) + i sin(5π/6) d) cos(π) + i sin(π)

29. If z₁ = 3 + i, z₂ = 2 – i, find z₁ – z₂. (KVS PGT 2018)

a) 1 – 2i b) 1 + 2i c) 5 d) 3 – i

30. Find the square roots of -1. (UP PGT 2020)

a) ±1 b) ±√2 c) ±i d) ±2i

31. If z = 4 + 3i, find |z|. (LT Grade 2022)

a) 7 b) 5 c) 4 d) 3

32. What is the argument of z = 1 – i√3? (KVS TGT 2021)

a) π/3 b) -π/3 c) π/6 d) -π/6

33. If z = 2(cos(π/4) + i sin(π/4)), find z². (NDA 2019)

a) 4 b) -4 c) 4i d) -4i

34. Find the real part of z = (2 – i)/(1 + i). (PCS 2022)

a) 1 b) 1/2 c) -1/2 d) 0

35. If z = -1 + i√3, find the polar form of z. (UP TGT 2019)

a) 2(cos(π/3) + i sin(π/3)) b) √2(cos(2π/3) + i sin(2π/3)) c) 2(cos(2π/3) + i sin(2π/3)) d) 2(cos(π/6) + i sin(π/6))

36. If z = 3i, find |z|². (KVS PGT 2020)

a) 3 b) 6 c) 9 d) 12

37. Find the conjugate of z = -2 + 4i. (NDA 2020)

a) 2 + 4i b) -2 – 4i c) -2 + 4i d) 2 – 4i

38. If z = 1 + i, find (z – z̅). (PCS 2019)

a) 2 b) -2i c) 2i d) 0

39. What is the modulus of z = cos(π/3) + i sin(π/3)? (UP TGT 2021)

a) √2 b) 1 c) 2 d) 1/√2

40. If z = 2 – 2i, find z². (KVS PGT 2019)

a) -8 b) 8 c) 8i d) -8i

41. Find the argument of z = -2 + 2i. (NDA 2021)

a) π/4 b) 3π/4 c) -π/4 d) π/2

42. If z = 1 + 2i, find |z|². (PCS 2020)

a) 3 b) 4 c) 5 d) 6

43. Find the real part of z = (1 + i)³. (UP TGT 2020)

a) 2 b) -2 c) 0 d) 1

44. If z = cos(π/4) + i sin(π/4), find z⁴. (KVS PGT 2021)

a) 1 b) i c) -1 d) -i

45. If z₁ = 2 + i, z₂ = 3 – i, find z₁/z₂. (NDA 2020)

a) (7 – i)/10 b) (7 + i)/10 c) (5 + i)/10 d) (7 – i)/5

46. Find the modulus of z = -1 – i√3. (UP PGT 2021)

a) √2 b) 1 c) 2 d) 2√2

47. If z = 2 + i, find the imaginary part of z². (KVS TGT 2020)

a) 2 b) 4 c) -4 d) 0

48. If z = cos(π/2) + i sin(π/2), find z³. (NDA 2021)

a) i b) 1 c) -i d) -1

49. If z₁ = 1 – i, z₂ = 2 + i, find z₁z₂. (PCS 2021)

a) 1 – i b) 3 – i c) 3 + i d) 1 + i

50. Find the square roots of 4i. (UP PGT 2022)

a) ±(2 + 2i) b) ±(√2 – i√2) c) ±(√2 + i√2) d) ±2i

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Complex Numbers Quiz for TGT, PGT, NDA, KVS, PCS, LT Grade, ETCE

1. What is the modulus of the complex number z = 3 + 4i? (KVS PGT 2018)

2. What is the conjugate of z = 2 – 3i? (NDA 2019)

3. If z = 1 + i, what is z²? (UP TGT 2021)

4. What is the argument of z = -1 + i? (KVS TGT 2018)

5. Express z = √3 + i in polar form. (NDA 2020)

6. If z = 2 + 3i, what is |z|²? (PCS 2019)

7. Find the real part of (1 + i)/(1 – i). (LT Grade 2020)

8. What is the cube of z = i using De Moivre’s theorem? (NDA 2021)

9. If z₁ = 2 + i, z₂ = 1 + 2i, find z₁z₂. (KVS PGT 2020)

10. Find the square roots of i. (UP PGT 2022)

11. If z = 3 – 4i, find 1/z. (KVS PGT 2019)

12. What is the modulus of z = -√2 + i√2? (NDA 2022)

13. If z = cos(π/3) + i sin(π/3), find z³. (UP TGT 2020)

14. Find the imaginary part of (2 + i)/(2 – i). (PCS 2021)

15. If |z| = 3 and arg(z) = π/4, what is z? (LT Grade 2021)

16. What is the sum of z = 5 + 2i and its conjugate? (KVS TGT 2019)

17. Find the modulus of z = -3 – 3i. (NDA 2018)

18. What is the argument of z = -1 – i? (UP PGT 2019)

19. If z = 2i, find z⁴. (KVS PGT 2021)

20. Express z = 1 – i in polar form. (NDA 2020)

21. If z₁ = 1 + i, z₂ = 1 – i, find |z₁ + z₂|. (PCS 2020)

22. What is the real part of z = (3 + 2i)²? (LT Grade 2019)

23. Find the cube roots of 1. (KVS PGT 2022)

24. If z = 2 + i, find z̅/z. (NDA 2021)

25. What is the polar form of z = -2? (UP TGT 2022)

26. If z = 1 + i√3, find |z|². (KVS TGT 2020)

27. Find the imaginary part of (1 – i)³. (PCS 2018)

28. If z = cos(π/6) + i sin(π/6), find z⁵. (NDA 2022)

29. If z₁ = 3 + i, z₂ = 2 – i, find z₁ – z₂. (KVS PGT 2018)

30. Find the square roots of -1. (UP PGT 2020)

31. If z = 4 + 3i, find |z|. (LT Grade 2022)

32. What is the argument of z = 1 – i√3? (KVS TGT 2021)

33. If z = 2(cos(π/4) + i sin(π/4)), find z². (NDA 2019)

34. Find the real part of z = (2 – i)/(1 + i). (PCS 2022)

35. If z = -1 + i√3, find the polar form of z. (UP TGT 2019)

36. If z = 3i, find |z|². (KVS PGT 2020)

37. Find the conjugate of z = -2 + 4i. (NDA 2020)

38. If z = 1 + i, find (z – z̅). (PCS 2019)

39. What is the modulus of z = cos(π/3) + i sin(π/3)? (UP TGT 2021)

40. If z = 2 – 2i, find z². (KVS PGT 2019)

41. Find the argument of z = -2 + 2i. (NDA 2021)

42. If z = 1 + 2i, find |z|². (PCS 2020)

43. Find the real part of z = (1 + i)³. (UP TGT 2020)

44. If z = cos(π/4) + i sin(π/4), find z⁴. (KVS PGT 2021)

45. If z₁ = 2 + i, z₂ = 3 – i, find z₁/z₂. (NDA 2020)

46. Find the modulus of z = -1 – i√3. (UP PGT 2021)

47. If z = 2 + i, find the imaginary part of z². (KVS TGT 2020)

48. If z = cos(π/2) + i sin(π/2), find z³. (NDA 2021)

49. If z₁ = 1 – i, z₂ = 2 + i, find z₁z₂. (PCS 2021)

50. Find the square roots of 4i. (UP PGT 2022)

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About the author

Chandra Shekhar

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