JEE Main - Algebra of complex numbers modulus and argument Online Test (MCQ Quiz)

1. What is the principal value of the argument of the complex number z = 1 + i?

A) π/4 B) π/2 C) 3π/4 D) π

2. If z = -1 - i, what is its argument?

A) π/4 B) 3π/4 C) -3π/4 D) -π/4

3. What is the modulus of the complex number z = 3 + 4i?

A) 5 B) 7 C) 12 D) 25

4. Calculate the modulus of z = -5 - 12i.

A) 7 B) 13 C) 17 D) 169

5. If z1 = 1 + i and z2 = 2 + 3i, what is z1 + z2?

A) 3 + 4i B) 1 + 4i C) 3 + 2i D) 2 + 5i

6. What is the product of z1 = 2 + i and z2 = 3 - i?

A) 7 + i B) 7 - i C) 5 + i D) 5 - i

7. If z = 4 - 3i, what is its conjugate?

A) 4 + 3i B) -4 + 3i C) -4 - 3i D) 3 - 4i

8. What is the argument of the complex number z = -√3 + i?

A) π/6 B) 5π/6 C) 7π/6 D) 11π/6

9. Find the modulus of z = cos(π/3) + i sin(π/3).

A) 1/2 B) √3/2 C) 1 D) 2

10. What is the argument of z = -1?

A) 0 B) π/2 C) π D) 3π/2

11. If z = 1 - i, what is its argument?

A) π/4 B) π/2 C) -π/4 D) -π/2

12. What is the modulus of z = 5?

A) 0 B) 5 C) 25 D) √5

13. Calculate the modulus of z = -2i.

A) 0 B) 2 C) 4 D) √2

14. If z1 = 3 + 2i and z2 = 1 - i, what is z1 - z2?

A) 2 + 3i B) 4 + i C) 2 + i D) 4 + 3i

15. What is the quotient of z1 = 1 + i and z2 = 1 - i?

A) 1 B) i C) -i D) 0

16. If z = a + bi, then z + z̄ is always:

A) Purely imaginary B) Purely real C) Zero D) Non-real

17. If z = a + bi, then z - z̄ is always:

A) Purely imaginary B) Purely real C) Zero D) Non-real

18. What is the argument of the complex number z = 1 + √3i?

A) π/6 B) π/3 C) 2π/3 D) 5π/6

19. Find the modulus of z = 2(cos(π/4) + i sin(π/4)).

A) √2 B) 2 C) 4 D) 1

20. What is the argument of z = i?

A) 0 B) π/2 C) π D) 3π/2

21. What is the principal argument of z = -1 - √3i?

A) 2π/3 B) 4π/3 C) -2π/3 D) -π/3

22. What is the modulus of z = 1 - i?

A) 0 B) 1 C) √2 D) 2

23. Calculate the modulus of z = -7i.

A) 0 B) 7 C) 49 D) √7

24. If z1 = 5 - 2i and z2 = 3 + 4i, what is z1 + z2?

A) 8 + 2i B) 2 - 6i C) 8 - 2i D) 2 + 6i

25. What is the product of z1 = 1 + 2i and z2 = 3 + i?

A) 1 + 7i B) 5 + 7i C) 3 + 7i D) 1 + 5i

26. If z = -2 + 5i, what is its conjugate?

A) 2 - 5i B) -2 - 5i C) 2 + 5i D) 5 - 2i

27. What is the argument of the complex number z = -1 + i?

A) π/4 B) 3π/4 C) 5π/4 D) 7π/4

28. Find the modulus of z = 3(cos(2π/3) + i sin(2π/3)).

A) 3/2 B) 3√3/2 C) 3 D) 9

29. What is the argument of z = -i?

A) 0 B) π/2 C) π D) 3π/2

30. What is the principal argument of z = -√3 - i?

A) π/6 B) 5π/6 C) 7π/6 D) -5π/6

31. What is the modulus of z = √3 + i?

A) 1 B) √2 C) 2 D) 4

32. Calculate the modulus of z = 8.

A) 0 B) 8 C) 64 D) √8

33. If z1 = 2 + 5i and z2 = 1 - 3i, what is z1 - z2?

A) 1 + 8i B) 3 + 2i C) 1 - 8i D) 3 - 2i

34. What is the quotient of z1 = 2 + 2i and z2 = 1 + i?

A) 1 B) 2 C) i D) 2i

35. If z = 3 - 4i, then z * z̄ is:

A) 9 B) 16 C) 25 D) 7

36. What is the argument of the complex number z = √3 - i?

A) π/6 B) π/3 C) -π/6 D) -π/3

37. Find the modulus of z = √2(cos(3π/4) + i sin(3π/4)).

A) √2 B) 2 C) 3√2/2 D) 1

38. What is the argument of z = 1?

A) 0 B) π/2 C) π D) 3π/2

39. What is the principal argument of z = 1 - i?

A) π/4 B) 3π/4 C) -π/4 D) -3π/4

40. What is the modulus of z = -6i?

A) 0 B) 6 C) 36 D) √6

41. If z1 = -1 + i and z2 = 1 - i, what is z1 + z2?

A) 0 B) 2i C) -2 D) 2

42. What is the product of z1 = 1 - i and z2 = 1 + i?

A) 0 B) 1 C) 2 D) i

43. If z = 7 + 0i, what is its conjugate?

A) 7 B) -7 C) 7i D) -7i

44. What is the argument of the complex number z = -1 - i?

A) π/4 B) 3π/4 C) 5π/4 D) 7π/4

45. Find the modulus of z = 5(cos(π) + i sin(π)).

A) 0 B) 1 C) 5 D) 5π

46. What is the argument of z = -1 + 0i?

A) 0 B) π/2 C) π D) 3π/2

47. What is the principal argument of z = -1 + √3i?

A) π/3 B) 2π/3 C) 4π/3 D) 5π/3

48. What is the modulus of z = 1 + √3i?

A) 1 B) √2 C) 2 D) 4

49. Calculate the modulus of z = 10i.

A) 0 B) 10 C) 100 D) √10

50. If z1 = 4 + 3i and z2 = 1 + 2i, what is z1 - z2?

A) 3 + i B) 5 + 5i C) 3 - i D) 5 - 5i

Algebra of complex numbers modulus and argument - Online Test

Test Results