Jump to a section

Mathematics - Complex Number

Practise 16 NEST (NISER) previous year questions on Complex Number, compiled from papers spanning 2011 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 NEST (NISER) tests.

Complex Number has been asked in 14 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 16 questions in all. 13% of them were easy, 75% moderate and 13% tough. Most of its questions came from 2022, with 2 questions that year. In the last three years (2024–2026) it had 2 questions across 4 papers, about 0.5 per paper.

The chapter's 9 topics are not weighted equally: Cube Root of Unity (4 questions, 25%), Algebra of complex numbers (3 questions, 19%), and Conjugate, modulus and argument (3 questions, 19%) have been asked the most. Cube Root of Unity has also led over the last five years, with 1 question. Algebra of complex numbers has produced the most tough questions (1).

  1. 1For a complex number , where , denote . The locus of satisfying in the complex plane is2026Conjugate, modulus and argument
  2. 2Let be a complex number such that but . Then is equal to2025De Moivres Theorem
  3. 3If , where and , then the value of is2023 (Session 2)Polar and Euler Form
  4. 4Let and be three distinct complex numbers. If , then2022 (Session 1)Cube Root of Unity
  5. 5For , a complex number is called an -th root of unity if . Then2022 (Session 2)nth roots of unity
  6. 6Let be a cube root of 1 , which is different from 1 . Then the value of is2021 (Session 1)Cube Root of Unity
  7. 7Let for each . Then2021 (Session 1)Algebra of complex numbers
  8. 8Let and be two nonzero complex numbers. For denotes the complex conjugate of . If the lines and are mutually perpendicular then2020 (Session 1)Geometry of Complex Number
  9. 9Let . If is an element of with argument , then the argument of is2019 (Session 1)Conjugate, modulus and argument
  10. 10Let and be complex numbers such that and . Then the complex numbers and always satisfy2018Conjugate, modulus and argument
  11. 11Let be the set of all complex numbers. Let and . Then2017Algebra of complex numbers
  12. 12The real and imaginary part of the complex number where are2016Algebra of complex numbers
  13. 13Let be the set of all complex numbers. Consider the function defined by . Then2015Rotation Theorem
  14. 14Let be a subset of complex numbers. Then, in the complex plane represents2014Locus Based on Distance Formula
  15. 15Let be the complex cube root of unity. Consider the set Then is2013Cube Root of Unity
  16. 16If is a complex cube root of unity, then2011Cube Root of Unity

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 16 questions compiled from NEST (NISER) papers spanning 2011 to 2026.

2.Are these questions only from NEST (NISER), or from other exams too?

These are NEST (NISER) 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 NEST (NISER) Mathematics?

Complex Number has appeared in 14 of the 16 years of NEST (NISER) papers covered here, with 16 questions across 15 papers - about one per paper it appears in.

4.What is the difficulty level of Complex Number questions in NEST (NISER)?

Of the 16 questions analysed for this chapter, 13% are easy, 75% moderate and 13% tough. 2022 had the most, with 2 questions.

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

These topics have carried the most weightage in Complex Number:

  • Cube Root of Unity - 4 questions (25%)
  • Algebra of complex numbers - 3 questions (19%)
  • Conjugate, modulus and argument - 3 questions (19%)
  • Algebra of complex numbers has produced the most tough questions (1).
6.Is Complex Number's weightage in NEST (NISER) going up or down?

Across all 15 papers analysed, Complex Number has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.5 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.