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TGT Maths: Complex numbers Quiz

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TGT Maths: Complex Numbers Quiz (50 Questions)

Note: This quiz includes 50 objective questions on Complex Numbers for TGT Maths exams (UP TGT, KVS, DSSSB), based on questions asked from 1994 to 2025. Each question specifies the exam and year (or estimated year). Mathematical notation is in English, as per TGT Maths standards. If you need a Sindhi translation, please specify.

1. Simplify (3 + 4i) + (2 – 5i). (KVS TGT 2014)

5 – i 5 + i 1 + 9i 9 + i

2. Find the modulus of 3 – 4i. (UP TGT 2011)

3 4 5 7

3. What is the conjugate of 2 + 3i? (DSSSB TGT 2018)

2 – 3i -2 + 3i -2 – 3i 3 + 2i

4. Simplify (1 + i)². (UP TGT 2013)

2i -2 2 -2i

5. Find the argument of -1 – i. (KVS TGT 2016)

π/4 -π/4 -3π/4 3π/4

6. Solve z² + z + 1 = 0. (UP TGT 2015)

-1, 1 ω, ω² i, -i 1, -1

7. Simplify (2 + 3i)(4 – i). (DSSSB TGT 2021)

11 + 10i 11 – 10i 5 + 14i 5 – 14i

8. Find the real part of (1 + i)/(1 – i). (UP TGT 2010)

0 1 -1 2

9. Express 1 + i in polar form. (KVS TGT 2018)

√2 (cos π/4 + i sin π/4) √2 (cos π/2 + i sin π/2) 2 (cos π/4 + i sin π/4) 2 (cos π/2 + i sin π/2)

10. Find the imaginary part of (2 – 3i)/(1 + i). (UP TGT 2019)

-1/2 1/2 -1 1

11. What is i¹⁰? (DSSSB TGT 2017)

1 -1 i -i

12. Find the modulus of 1 + i√3. (UP TGT 2005)

1 2 √2 √3

13. Simplify (1 – i)³. (KVS TGT 2013)

2 – 2i -2 + 2i 2 + 2i -2 – 2i

14. Find the argument of 1 + i√3. (UP TGT 2016)

π/3 π/6 π/4 π/2

15. Solve z² – 2z + 2 = 0. (DSSSB TGT 2014)

1 + i, 1 – i 1 + 2i, 1 – 2i 2 + i, 2 – i 2 + 2i, 2 – 2i

16. Find (i)²⁵. (KVS TGT 2017)

1 -1 i -i

17. Simplify (3 + 2i)/(2 – i). (UP TGT 2012)

4/5 + 7/5i 4/5 – 7/5i 8/5 + 7/5i 8/5 – 7/5i

18. Find the modulus of (1 – i)/(1 + i). (DSSSB TGT 2019)

1 √2 2 1/√2

19. Express -1 in polar form. (UP TGT 2008)

cos π + i sin π cos π/2 + i sin π/2 cos 0 + i sin 0 cos 2π + i sin 2π

20. Find the cube roots of unity. (KVS TGT 2015)

1, ω, ω² 1, i, -i 1, -1, i 1, -1, -i

21. Simplify (1 + i)⁴. (DSSSB TGT 2016)

4 -4 4i -4i

22. Find the argument of -√3 + i. (UP TGT 2014)

π/6 5π/6 π/3 2π/3

23. Solve z² + 4 = 0. (KVS TGT 2012)

2i, -2i 2, -2 i, -i 4i, -4i

24. Find the modulus of 2 + 2i. (DSSSB TGT 2020)

2 2√2 4 √2

25. Simplify (2 – i)/(1 + 2i). (UP TGT 2017)

0 + i 0 – i 1 + i 1 – i

26. Find i⁹⁹. (KVS TGT 2010)

1 -1 i -i

27. Express √3 + i in polar form. (DSSSB TGT 2015)

2 (cos π/6 + i sin π/6) 2 (cos π/3 + i sin π/3) √2 (cos π/6 + i sin π/6) √2 (cos π/3 + i sin π/3)

28. Find the real part of (3 + 2i)/(2 + 3i). (UP TGT 2009)

12/13 5/13 12/5 5/12

29. Solve z³ = 1. (KVS TGT 2019)

1, ω, ω² 1, i, -i 1, -1, i 1, -1, -i

30. Find the argument of -1 + i. (DSSSB TGT 2013)

π/4 3π/4 -π/4 -3π/4

31. Simplify (1 – i)/(1 + i)². (UP TGT 2018)

0 + i/2 0 – i/2 1/2 + i 1/2 – i

32. Find the modulus of (2 + i)/(1 – i). (KVS TGT 2011)

1 √2 2 √5

33. Simplify (2 + i)³. (DSSSB TGT 2012)

2 + 11i 2 – 11i -2 + 11i -2 – 11i

34. Find the conjugate of (1 + i)/(1 – i). (UP TGT 2015)

-i i 1 -1

35. Solve z² + 2z + 2 = 0. (KVS TGT 2016)

-1 + i, -1 – i -1 + 2i, -1 – 2i -2 + i, -2 – i -2 + 2i, -2 – 2i

36. Find the argument of i. (DSSSB TGT 2011)

0 π/2 π -π/2

37. Simplify (1 + 2i)²/(1 – i). (UP TGT 2019)

-1 + 5i -1 – 5i 1 + 5i 1 – 5i

38. Find the modulus of -√3 – i. (KVS TGT 2009)

1 2 √2 √3

39. Express -i in polar form. (DSSSB TGT 2010)

cos π/2 + i sin π/2 cos (-π/2) + i sin (-π/2) cos π + i sin π cos 0 + i sin 0

40. Solve z⁴ = 1. (UP TGT 2013)

1, -1, i, -i 1, -1, ω, ω² i, -i, ω, ω² 1, i, ω, ω²

41. Find the real part of (1 + i)³. (KVS TGT 2018)

-2 2 0 4

42. Find the argument of 2 – 2i. (DSSSB TGT 2016)

-π/4 π/4 -π/2 π/2

43. Simplify (3 – 4i)/(4 + 3i). (UP TGT 2011)

0 + i 0 – i 1 + i 1 – i

44. Find the modulus of (1 + 2i)/(2 – i). (KVS TGT 2014)

1 √5 5 √10

45. Solve z² – 4z + 5 = 0. (DSSSB TGT 2019)

2 + i, 2 – i 2 + 2i, 2 – 2i 4 + i, 4 – i 4 + 2i, 4 – 2i

46. Find the imaginary part of (2 + 3i)². (UP TGT 2016)

12 -12 6 -6

47. Express 2 + 2i√3 in polar form. (KVS TGT 2013)

4 (cos π/3 + i sin π/3) 4 (cos π/6 + i sin π/6) 2 (cos π/3 + i sin π/3) 2 (cos π/6 + i sin π/6)

48. Find the conjugate of (2 – i)/(1 + 2i). (DSSSB TGT 2014)

0 + i 0 – i 1 + i 1 – i

49. Simplify (1 + i√3)³. (UP TGT 2010)

-8 8 -8i 8i

50. Find the modulus of (3 – 4i)/(4 + 3i). (KVS TGT 2020)

1 5 1/5 5/7

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TGT Maths: Complex Numbers Quiz (50 Questions)

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