Complex Numbers: 50 Questions for UP TGT Exam
1. What is the value of i²?
Answer: -1
2. Simplify (3 + 4i) + (2 – 5i).
Answer: 5 – i
3. Find the conjugate of 7 – 3i.
Answer: 7 + 3i
4. What is the modulus of 3 + 4i?
Answer: 5
5. Simplify (2 + 3i)(4 – i).
Answer: 11 + 10i
6. Divide (5 + 15i) by (2 – i).
Answer: 3 + 7i
7. What is the argument of -1 – i in radians?
Answer: -3π/4
8. Express 1 + i in polar form.
Answer: √2 (cos(π/4) + i sin(π/4))
9. Find i^17.
Answer: i
10. Solve z² = -4.
Answer: z = ±2i
11. What is the real part of 6 – 8i?
Answer: 6
12. What is the imaginary part of -2 + 5i?
Answer: 5
13. Simplify (1 – i)³.
Answer: -2 – 2i
14. Find the modulus of -5 + 12i.
Answer: 13
15. What is the conjugate of -4i?
Answer: 4i
16. Simplify (2 + i)/(1 + i).
Answer: 1.5 – 0.5i
17. Find the argument of 1 – i.
Answer: -π/4
18. Express -√3 + i in polar form.
Answer: 2 (cos(5π/6) + i sin(5π/6))
19. Find (1 + i)^4 using De Moivre’s theorem.
Answer: -4
20. Solve z² + 2z + 2 = 0.
Answer: z = -1 ± i
21. What is the modulus of i?
Answer: 1
22. Simplify (3 – 2i) – (1 + 3i).
Answer: 2 – 5i
23. Find the square roots of -9.
Answer: ±3i
24. What is i^10?
Answer: -1
25. Find the conjugate of 2 + 0i.
Answer: 2
26. Simplify (4 + 3i)(4 – 3i).
Answer: 25
27. Find the modulus of -1 + i.
Answer: √2
28. What is the argument of -√2 – i√2?
Answer: -3π/4
29. Express 2i in polar form.
Answer: 2 (cos(π/2) + i sin(π/2))
30. Simplify (1 + i)/(1 – i).
Answer: i
31. Find (1 – i)^3.
Answer: 2 – 2i
32. Solve z² = 1 + i.
Answer: z = ±(√2/2 + i√2/2)
33. What is the real part of (2 + 3i)²?
Answer: -5
34. What is the imaginary part of (1 – 2i)²?
Answer: -4
35. Find the modulus of 3 – 4i.
Answer: 5
36. Simplify (2i)³.
Answer: -8i
37. Find the argument of -2.
Answer: π
38. Express -1 in polar form.
Answer: 1 (cos(π) + i sin(π))
39. Find (√3 + i)^3 using De Moivre’s theorem.
Answer: -8
40. Solve z² + 4 = 0.
Answer: z = ±2i
41. What is the conjugate of 0 + 5i?
Answer: -5i
42. Simplify (3 + 2i) + (-3 – 2i).
Answer: 0
43. Find the modulus of 1 + i√3.
Answer: 2
44. What is the argument of √3 + i?
Answer: π/6
45. Simplify (2 + i)/(2 – i).
Answer: 3/5 + 4i/5
46. Find i^25.
Answer: i
47. Solve z² = -16.
Answer: z = ±4i
48. Express -2 + 2i in polar form.
Answer: 2√2 (cos(3π/4) + i sin(3π/4))
49. Find (1 + i)^2.
Answer: 2i
50. What is the modulus of 0 + i?
Answer: 1
