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Mathematics - Complex Number

Practise 220 JEE Main previous year questions on Complex Number, compiled from papers spanning 2002 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 JEE Main tests.

Complex Number has been asked in 25 of the 25 years of JEE Main papers analysed (2002–2026), with 220 questions in all. 13% of them were easy, 54% moderate and 33% tough. Most of its questions came from 2021, with 29 questions that year. In the last three years (2024–2026) it had 51 questions across 49 papers, about 1 per paper.

The chapter's 9 topics are not weighted equally: Conjugate, modulus and argument (70 questions, 32%), Geometry of Complex Number (61 questions, 28%), and Algebra of complex numbers (44 questions, 20%) have been asked the most. Conjugate, modulus and argument has also led over the last five years, with 42 questions. Geometry of Complex Number has produced the most tough questions (32).

  1. 1The number of values of , satisfying the equations and , is:08 Apr, 2026 (E)Locus Based on Distance Formula
  2. 2Let the set of all values of such that the equation , , has at least one solution, be the interval . Then is equal to:06 Apr, 2026 (M)Algebra of complex numbers
  3. 3Let . Then is equal to :06 Apr, 2026 (E)De Moivres Theorem
  4. 4Let be the distinct solutions of the equation . Then is equal to :05 Apr, 2026 (E)Conjugate, modulus and argument
  5. 5Let be a complex number such that and . Then is equal to:04 Apr, 2026 (M)Locus Based on Distance Formula
  6. 6Let . Then is equal to:04 Apr, 2026 (E)Conjugate, modulus and argument
  7. 7Let and be real numbers such that , . Then the value of is :02 Apr, 2026 (M)Algebra of complex numbers
  8. 8Let the circles and , , be such that lies within . If moves on , moves on and , then is equal to:02 Apr, 2026 (E)Locus Based on Distance Formula
  9. 9Let be a complex number such that and . Then the value of is equal to28 Jan, 2026 (M)Locus Based on Distance Formula
  10. 10Let and . Then the max and is :28 Jan, 2026 (E)Locus Based on Distance Formula
  11. 11Let , where . If , then is equal to24 Jan, 2026 (E)Conjugate, modulus and argument
  12. 12Let be a set of complex numbers. Then is equal to :23 Jan, 2026 (M)Conjugate, modulus and argument
  13. 13If , then is equal to23 Jan, 2026 (E)Common Tangent
  14. 14Let and . If , then is22 Jan, 2026 (M)Cube Root of Unity
  15. 15Let . Then is equal to:22 Jan, 2026 (E)Conjugate, modulus and argument
  16. 16If , then the value of is:21 Jan, 2026 (M)Cube Root of Unity
  17. 17Let be the complex number satisfying and having maximum positive principal argument. Then is equal to :21 Jan, 2026 (E)Conjugate, modulus and argument
  18. 18Let Then is equal to08 Apr, 2025 (E)Conjugate, modulus and argument
  19. 19Among the statements (S1) : The set and is purely real} contains exactly two elements, and (S2) : The set and is purely imaginary contains i07 Apr, 2025 (M)Conjugate, modulus and argument
  20. 20If the locus of , such that is a circle of radius and center then is equal to :07 Apr, 2025 (E)Geometry of Complex Number
  21. 21Let , and . Then is equal to ________ .04 Apr, 2025 (M)Locus Based on Distance Formula
  22. 22Let the product of and be , . Let p and q be the maximum and the minimum values of respectively.04 Apr, 2025 (E)Algebra of complex numbers
  23. 23If is a root of the equation and , then n is equal to04 Apr, 2025 (E)Cube Root of Unity
  24. 24Let be such that . Then the sum of all possible values of is03 Apr, 2025 (M)Algebra of complex numbers
  25. 25If are the vertices of an equilateral triangle, whose centroid is , then is equal to03 Apr, 2025 (E)Geometry of Complex Number
  26. 26Let be a complex number such that . If , then the maximum distance of from the circle is:02 Apr, 2025 (M)Geometry of Complex Number
  27. 27Let \( |z_1-8-2 i | 1\) and \( |z_2-2+6 i | 2, z_1, z_2 {C}\). Then the minimum value of \( |z_1-z_2 |\) is :29 Jan, 2025 (M)Geometry of Complex Number
  28. 28Let integers be such that . Then the number of all possible ordered pairs (a, b), for which and , where and are the roots of , is equal to _29 Jan, 2025 (E)Cube Root of Unity
  29. 29Let be the origin, the point be , the point be such that and . Then28 Jan, 2025 (M)Conjugate, modulus and argument
  30. 30If and are the roots of , then is equal to :28 Jan, 2025 (E)Algebra of complex numbers
  31. 31If and are the roots of the equation , where , then is equal to24 Jan, 2025 (M)Conjugate, modulus and argument
  32. 32Let , be the equation of a circle with center at . If the area of the triangle, whose vertices are at the points and is 11 square units, the23 Jan, 2025 (M)Geometry of Complex Number
  33. 33The number of complex numbers , satisfying and , is :23 Jan, 2025 (E)Algebra of complex numbers
  34. 34Let be the roots of the equation with . Let . If and , then is equal to .23 Jan, 2025 (E)Algebra of complex numbers
  35. 35Let and be three complex numbers on the circle with and . If , then the value of is :22 Jan, 2025 (M)Conjugate, modulus and argument
  36. 36Let the curve , divide the region into two parts of areas and . Then equals :22 Jan, 2025 (E)Geometry of Complex Number
  37. 37The sum of the square of the modulus of the elements in the set is ________09 Apr, 2024 (M)Conjugate, modulus and argument
  38. 38Let be a complex number such that the real part of is zero. Then, the maximum value of is equal to09 Apr, 2024 (E)Conjugate, modulus and argument
  39. 39Let be a complex number such that and . Then the value of is08 Apr, 2024 (M)Algebra of complex numbers
  40. 40The sum of all possible values of , for which is purely imaginary, is equal08 Apr, 2024 (E)Conjugate, modulus and argument
  41. 41If are two distinct complex number such that , then06 Apr, 2024 (E)Geometry of Complex Number
  42. 42Consider the following two statements : Statement I : For any two non-zero complex numbers , Statement II : If are three distinct complex nu05 Apr, 2024 (M)Algebra of complex numbers
  43. 43Let and . Then the area of the region is :05 Apr, 2024 (E)Conjugate, modulus and argument
  44. 44Let and be the sum and the product of all the non-zero solutions of the equation , C. Then is equal to :04 Apr, 2024 (M)Conjugate, modulus and argument
  45. 45The area (in sq. units) of the region is04 Apr, 2024 (E)Conjugate, modulus and argument
  46. 46Let P = z ∈ ℂ : z + 2 − 3 i ≤ 1 and Q = z ∈ ℂ : z 1 + i + z ¯ 1 − i ≤ − 8 . Let in P ∩ Q , z − 3 + 2 i be maximum and minimum at z 1 and z 201 Feb, 2024 (M)Geometry of Complex Number
  47. 47Let S = z ∈ C : z − 1 = 1 and 2 − 1 z + z ¯ - i z - z ¯ = 2 2 . Let z 1 , z 2 ∈ S be such that z 1 = max z ∈ s z and z 2 = min z ∈ s z . The01 Feb, 2024 (M)Geometry of Complex Number
  48. 48If z is a complex number such that z ≤ 1 , then the minimum value of z + 1 2 3 + 4 i is:01 Feb, 2024 (E)Conjugate, modulus and argument
  49. 49If α denotes the number of solutions of 1 − i x = 2 x and β = z arg z , where z = π 4 1 + i 4 1 − π · i π + i + π − i 1 + π · i , i = − 1 , 31 Jan, 2024 (M)Conjugate, modulus and argument
  50. 50Let z 1 and z 2 be two complex number such that z 1 + z 2 = 5 and z 1 3 + z 2 3 = 20 + 15 i . Then z 1 4 + z 2 4 equals-31 Jan, 2024 (E)Conjugate, modulus and argument

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 220 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

3.Is Complex Number an important chapter for JEE Main Mathematics?

Complex Number has appeared in 25 of the 25 years of JEE Main papers covered here, with 220 questions across 191 papers - about one per paper it appears in.

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

Of the 220 questions analysed for this chapter, 13% are easy, 54% moderate and 33% tough. 2021 had the most, with 29 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 - 70 questions (32%)
  • Geometry of Complex Number - 61 questions (28%)
  • Algebra of complex numbers - 44 questions (20%)
  • Geometry of Complex Number has produced the most tough questions (32).
6.Is Complex Number's weightage in JEE Main going up or down?

Across all 191 papers analysed, Complex Number has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.