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Mathematics - Complex Number

Practise 133 NDA previous year questions on Complex Number, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Complex Number has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 133 questions in all. 25% of them were easy, 71% moderate and 4% tough. Most of its questions came from 2016, with 12 questions that year. In the last three years (2024–2026) it had 21 questions across 5 papers, about 4.2 per paper.

The chapter's 9 topics are not weighted equally: Conjugate, modulus and argument (49 questions, 37%), Cube Root of Unity (27 questions, 20%), and De Moivres Theorem (20 questions, 15%) have been asked the most. Conjugate, modulus and argument has also led over the last five years, with 12 questions. Conjugate, modulus and argument has produced the most tough questions (4).

  1. 1Consider the following inequalities : I. II. 4+3i>3+4i i= {-1}$ How many of the above are valid ?2026 (Phase 1)Algebra of complex numbers
  2. 2Let and be complex numbers such that is purely imaginary. What is equal to ?2026 (Phase 1)Conjugate, modulus and argument
  3. 3If , , are cube roots of , then what is equal to ?2026 (Phase 1)Cube Root of Unity
  4. 4If , , are the cube roots of unity, then what is equal to ?2026 (Phase 1)Cube Root of Unity
  5. 5If is a non-real cube root of unity, then what is a root of the following equation?2025 (Phase 1)Cube Root of Unity
  6. 6What is equal to?2025 (Phase 1)Conjugate, modulus and argument
  7. 7If is a complex number, then what is equal to?2025 (Phase 1)Conjugate, modulus and argument
  8. 8If , then what is the value of ?2025 (Phase 2)Cube Root of Unity
  9. 9If , where , then what is the smallest positive value of ?2025 (Phase 2)Algebra of complex numbers
  10. 10Let , , be three cube roots of unity. If , , , then what is equal to?2025 (Phase 2)Cube Root of Unity
  11. 11If , then what is equal to?2025 (Phase 2)Polar and Euler Form
  12. 12If is any complex number and , where , then what is the value of2024 (Phase 1)Conjugate, modulus and argument
  13. 13If and are the cube roots of unity, then what is the value of ?2024 (Phase 1)Cube Root of Unity
  14. 14Let and be two complex numbers such that , then what is equal to?2024 (Phase 1)Conjugate, modulus and argument
  15. 15If is a cube root of unity, then what are the solution of ?2024 (Phase 1)Cube Root of Unity
  16. 16What is equal to, where ?2024 (Phase 1)De Moivres Theorem
  17. 17If is a cube root of unity, then what is equal to?2024 (Phase 2)De Moivres Theorem
  18. 18What is the value of the sum where ?2024 (Phase 2)Algebra of complex numbers
  19. 19If then what is2024 (Phase 2)De Moivres Theorem
  20. 20Paragraph: Let and be any two complex numbers such that Question: What is the value of ?2024 (Phase 2)Conjugate, modulus and argument
  21. 21Paragraph: Let and be any two complex numbers such that Question: What is the value of ?2024 (Phase 2)Algebra of complex numbers
  22. 22If is a non-real cube root of 1 , then what is the value of2023 (Phase 1)Cube Root of Unity
  23. 23If and are the distinct roots of equation , then what is the value of ?2023 (Phase 1)De Moivres Theorem
  24. 24If where , then what is the argument of ?2023 (Phase 1)Conjugate, modulus and argument
  25. 25If is a complex number such that is purely imaginary, then what is equal to?2023 (Phase 1)Conjugate, modulus and argument
  26. 26If , where then the locus of is a pair of :2023 (Phase 2)Locus Based on Distance Formula
  27. 27What is the value of , where ?2023 (Phase 2)Algebra of complex numbers
  28. 28Which one of the following is a square root of ?2023 (Phase 2)Algebra of complex numbers
  29. 29Consider equation-I: and equation -II: What are the roots of equation – I?2023 (Phase 2)Cube Root of Unity
  30. 30Consider equation-I: and equation -II: Which of the following is a root of equation-I?2023 (Phase 2)Cube Root of Unity
  31. 31Consider equation-I: and equation -II: What is the number of common roots of equation-I and equation-II?2023 (Phase 2)nth roots of unity
  32. 32What is the principal argument of where ?2022 (Phase 1)Conjugate, modulus and argument
  33. 33What is the modulus of ?2022 (Phase 1)De Moivres Theorem
  34. 34Paragraph: Let where Question: What is the modulus of ?2022 (Phase 2)Conjugate, modulus and argument
  35. 35Paragraph: Let where Question: What is angle such that is purely real? where is an integer2022 (Phase 2)Conjugate, modulus and argument
  36. 36Paragraph: Let where Question: What is angle such that is purely imaginary? where is an integer2022 (Phase 2)Conjugate, modulus and argument
  37. 37The smallest positive integer for which where , is2021 (Phase 1)De Moivres Theorem
  38. 38If , where , then what is the modulus of ?2021 (Phase 1)Conjugate, modulus and argument
  39. 39Consider the following in respect of a complex number : 1. 2. Which of the above is/are correct?2021 (Phase 1)Conjugate, modulus and argument
  40. 40Consider the following statements in respect of an arbitrary complex number : 1. The difference of and its conjugate is an imaginary number.2021 (Phase 1)Conjugate, modulus and argument
  41. 41What is the modulus of the complex number , where and ?2021 (Phase 1)Conjugate, modulus and argument
  42. 42Consider the following statements in respect of the roots of the equation : 1. The roots are non-collinear. 2. The roots lie on a circle of 2021 (Phase 2)nth roots of unity
  43. 43If , then what is the value of2021 (Phase 2)Cube Root of Unity
  44. 44What is equal to, where ?2021 (Phase 2)De Moivres Theorem
  45. 45If , where , then what does the equation represent?2021 (Phase 2)Geometry of Complex Number
  46. 46Which one of the following is a square root of , where ? where .2021 (Phase 2)Algebra of complex numbers
  47. 47If , then how many values does have for different ?2021 (Phase 2)Power of iota
  48. 48What is the modulus of the complex number , where ?2020Conjugate, modulus and argument
  49. 49What is the argument of the complex number , where ?2020Conjugate, modulus and argument
  50. 50The common roots of the equations and are2019 (Phase 1)nth roots of unity

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 133 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA questions specifically for the Complex Number chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Complex Number an important chapter for NDA Mathematics?

Complex Number has appeared in 17 of the 17 years of NDA papers covered here, with 133 questions across 32 papers - about 4 per paper it appears in.

4.What is the difficulty level of Complex Number questions in NDA?

Of the 133 questions analysed for this chapter, 25% are easy, 71% moderate and 4% tough. 2016 had the most, with 12 questions.

5.Which topics in Complex Number should I focus on?

These topics have carried the most weightage in Complex Number:

  • Conjugate, modulus and argument - 49 questions (37%)
  • Cube Root of Unity - 27 questions (20%)
  • De Moivres Theorem - 20 questions (15%)
  • Conjugate, modulus and argument has produced the most tough questions (4).
6.Is Complex Number's weightage in NDA going up or down?

Across all 32 papers analysed, Complex Number has averaged about 4.2 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 4.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.