Algebra of complex numbers modulus and argument - One Line Questions

1. Find the modulus of z = 2(cos(π/4) + i sin(π/4)). — 2
2. Find the modulus of z = √2(cos(3π/4) + i sin(3π/4)). — √2
3. What is the argument of z = -1? — π
4. What is the modulus of z = 5? — 5
5. Calculate the modulus of z = -2i. — 2
6. What is the argument of z = i? — π/2
7. What is the modulus of z = 1 - i? — √2
8. Calculate the modulus of z = -7i. — 7
9. What is the argument of z = -i? — 3π/2
10. Calculate the modulus of z = 8. — 8
11. What is the argument of z = 1? — 0
12. What is the modulus of z = -6i? — 6
13. If z1 = -1 + i and z2 = 1 - i, what is z1 + z2? — 0
14. What is the product of z1 = 1 - i and z2 = 1 + i? — 2
15. Find the modulus of z = 5(cos(π) + i sin(π)). — 5
16. What is the argument of z = -1 + 0i? — π
17. Calculate the modulus of z = 10i. — 10
18. What is the quotient of z1 = 1 + i and z2 = 1 - i? — i
19. What is the modulus of z = √3 + i? — 2
20. What is the quotient of z1 = 2 + 2i and z2 = 1 + i? — 2
21. What is the modulus of z = 1 + √3i? — 2
22. What is the product of z1 = 1 + 2i and z2 = 3 + i? — 5 + 7i
23. If z1 = 2 + 5i and z2 = 1 - 3i, what is z1 - z2? — 3 + 2i
24. What is the quotient of z1 = 1 + i and z2 = √2? — 1/√2 + i/√2
25. Find the modulus of z = cos(π/3) + i sin(π/3). — 1
26. If z = -2 + 5i, what is its conjugate? — -2 - 5i
27. If z1 = 3 + 2i and z2 = 1 - i, what is z1 - z2? — 2 + 3i
28. What is the principal argument of z = -1 - √3i? — -2π/3
29. If z1 = 1 + i and z2 = 2 + 3i, what is z1 + z2? — 3 + 4i
30. If z1 = 4 + 3i and z2 = 1 + 2i, what is z1 - z2? — 3 + i
31. Find the modulus of z = 3(cos(2π/3) + i sin(2π/3)). — 3
32. If z = 4 - 3i, what is its conjugate? — 4 + 3i
33. What is the modulus of the complex number z = 3 + 4i? — 5
34. Calculate the modulus of z = -5 - 12i. — 13
35. If z = 7 + 0i, what is its conjugate? — 7
36. What is the product of z1 = 2 + i and z2 = 3 - i? — 7 + i
37. If z1 = 5 - 2i and z2 = 3 + 4i, what is z1 + z2? — 8 + 2i
38. If z = 3 - 4i, then z * z̄ is: — 25
39. If z = a + bi, then z + z̄ is always: — Purely real
40. If z = a + bi, then z - z̄ is always: — Purely imaginary
41. What is the principal argument of z = -1 + √3i? — 2π/3
42. What is the principal value of the argument of the complex number z = 1 + i? — π/4
43. If z = -1 - i, what is its argument? — -3π/4
44. If z = 1 - i, what is its argument? — -π/4
45. What is the argument of the complex number z = -1 + i? — 3π/4
46. What is the principal argument of z = 1 - i? — -π/4
47. What is the argument of the complex number z = -1 - i? — 5π/4
48. What is the argument of the complex number z = -√3 + i? — 5π/6
49. What is the argument of the complex number z = 1 + √3i? — π/3
50. What is the principal argument of z = -√3 - i? — -5π/6
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