Algebra of complex numbers modulus and argument - Question Bank

1. What is the quotient of z1 = 1 + i and z2 = √2?
A) 1/√2 + i/√2
B) 1/√2 - i/√2
C) √2 + i√2
D) √2 - i√2
2. If z1 = 4 + 3i and z2 = 1 + 2i, what is z1 - z2?
A) 3 + i
B) 5 + 5i
C) 3 - i
D) 5 - 5i
3. Calculate the modulus of z = 10i.
A) 0
B) 10
C) 100
D) √10
4. What is the modulus of z = 1 + √3i?
A) 1
B) √2
C) 2
D) 4
5. What is the principal argument of z = -1 + √3i?
A) π/3
B) 2π/3
C) 4π/3
D) 5π/3
6. What is the argument of z = -1 + 0i?
A) 0
B) π/2
C) π
D) 3π/2
7. Find the modulus of z = 5(cos(π) + i sin(π)).
A) 0
B) 1
C) 5
D) 5π
8. What is the argument of the complex number z = -1 - i?
A) π/4
B) 3π/4
C) 5π/4
D) 7π/4
9. If z = 7 + 0i, what is its conjugate?
A) 7
B) -7
C) 7i
D) -7i
10. What is the product of z1 = 1 - i and z2 = 1 + i?
A) 0
B) 1
C) 2
D) i
11. If z1 = -1 + i and z2 = 1 - i, what is z1 + z2?
A) 0
B) 2i
C) -2
D) 2
12. What is the modulus of z = -6i?
A) 0
B) 6
C) 36
D) √6
13. What is the principal argument of z = 1 - i?
A) π/4
B) 3π/4
C) -π/4
D) -3π/4
14. What is the argument of z = 1?
A) 0
B) π/2
C) π
D) 3π/2
15. Find the modulus of z = √2(cos(3π/4) + i sin(3π/4)).
A) √2
B) 2
C) 3√2/2
D) 1
16. What is the argument of the complex number z = √3 - i?
A) π/6
B) π/3
C) -π/6
D) -π/3
17. If z = 3 - 4i, then z * z̄ is:
A) 9
B) 16
C) 25
D) 7
18. What is the quotient of z1 = 2 + 2i and z2 = 1 + i?
A) 1
B) 2
C) i
D) 2i
19. If z1 = 2 + 5i and z2 = 1 - 3i, what is z1 - z2?
A) 1 + 8i
B) 3 + 2i
C) 1 - 8i
D) 3 - 2i
20. Calculate the modulus of z = 8.
A) 0
B) 8
C) 64
D) √8
21. What is the modulus of z = √3 + i?
A) 1
B) √2
C) 2
D) 4
22. What is the principal argument of z = -√3 - i?
A) π/6
B) 5π/6
C) 7π/6
D) -5π/6
23. What is the argument of z = -i?
A) 0
B) π/2
C) π
D) 3π/2
24. Find the modulus of z = 3(cos(2π/3) + i sin(2π/3)).
A) 3/2
B) 3√3/2
C) 3
D) 9
25. What is the argument of the complex number z = -1 + i?
A) π/4
B) 3π/4
C) 5π/4
D) 7π/4
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 product of z1 = 1 + 2i and z2 = 3 + i?
A) 1 + 7i
B) 5 + 7i
C) 3 + 7i
D) 1 + 5i
28. If z1 = 5 - 2i and z2 = 3 + 4i, what is z1 + z2?
A) 8 + 2i
B) 2 - 6i
C) 8 - 2i
D) 2 + 6i
29. Calculate the modulus of z = -7i.
A) 0
B) 7
C) 49
D) √7
30. What is the modulus of z = 1 - i?
A) 0
B) 1
C) √2
D) 2
31. What is the principal argument of z = -1 - √3i?
A) 2π/3
B) 4π/3
C) -2π/3
D) -π/3
32. What is the argument of z = i?
A) 0
B) π/2
C) π
D) 3π/2
33. Find the modulus of z = 2(cos(π/4) + i sin(π/4)).
A) √2
B) 2
C) 4
D) 1
34. What is the argument of the complex number z = 1 + √3i?
A) π/6
B) π/3
C) 2π/3
D) 5π/6
35. If z = a + bi, then z - z̄ is always:
A) Purely imaginary
B) Purely real
C) Zero
D) Non-real
36. If z = a + bi, then z + z̄ is always:
A) Purely imaginary
B) Purely real
C) Zero
D) Non-real
37. What is the quotient of z1 = 1 + i and z2 = 1 - i?
A) 1
B) i
C) -i
D) 0
38. If z1 = 3 + 2i and z2 = 1 - i, what is z1 - z2?
A) 2 + 3i
B) 4 + i
C) 2 + i
D) 4 + 3i
39. Calculate the modulus of z = -2i.
A) 0
B) 2
C) 4
D) √2
40. What is the modulus of z = 5?
A) 0
B) 5
C) 25
D) √5
41. If z = 1 - i, what is its argument?
A) π/4
B) π/2
C) -π/4
D) -π/2
42. What is the argument of z = -1?
A) 0
B) π/2
C) π
D) 3π/2
43. Find the modulus of z = cos(π/3) + i sin(π/3).
A) 1/2
B) √3/2
C) 1
D) 2
44. What is the argument of the complex number z = -√3 + i?
A) π/6
B) 5π/6
C) 7π/6
D) 11π/6
45. If z = 4 - 3i, what is its conjugate?
A) 4 + 3i
B) -4 + 3i
C) -4 - 3i
D) 3 - 4i
46. What is the product of z1 = 2 + i and z2 = 3 - i?
A) 7 + i
B) 7 - i
C) 5 + i
D) 5 - i
47. If z1 = 1 + i and z2 = 2 + 3i, what is z1 + z2?
A) 3 + 4i
B) 1 + 4i
C) 3 + 2i
D) 2 + 5i
48. Calculate the modulus of z = -5 - 12i.
A) 7
B) 13
C) 17
D) 169
49. What is the modulus of the complex number z = 3 + 4i?
A) 5
B) 7
C) 12
D) 25
50. If z = -1 - i, what is its argument?
A) π/4
B) 3π/4
C) -3π/4
D) -π/4
All Question Banks
E-Book Algebra of complex numbers modulus and argument One Line Questions Algebra of complex numbers modulus and argument Online Test Algebra of complex numbers modulus and argument