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Mathematics - Complex Number

Practise 59 WBJEE previous year questions on Complex Number, compiled from papers spanning 2009 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 WBJEE tests.

Complex Number has been asked in 18 of the 18 years of WBJEE papers analysed (2009–2026), with 59 questions in all. 27% of them were easy, 54% moderate and 19% tough. Most of its questions came from 2014, with 6 questions that year. In the last three years (2024–2026) it had 8 questions across 3 papers, about 2.7 per paper.

The chapter's 10 topics are not weighted equally: Conjugate, modulus and argument (20 questions, 34%), Polar and Euler Form (9 questions, 15%), and Geometry of Complex Number (9 questions, 15%) have been asked the most. Over the last five years the most frequent topics have been Geometry of Complex Number (5), Conjugate, modulus and argument (4), and Cube Root of Unity (2). Geometry of Complex Number has produced the most tough questions (5).

  1. 1The expression represents2026nth roots of unity
  2. 2The total number of polynomials of the form which is divisible by , where is2026Conjugate, modulus and argument
  3. 3Let be the roots of the equation , where the coefficients and may be complex numbers and also let represent respectively in the complex plan2026Rotation Theorem
  4. 4If are complex numbers such that is a purely imaginary number, then the value of is2025Conjugate, modulus and argument
  5. 5Let be a cubic root of unity. Then the minimum value of the set are distinct non-zero integers} equals2025Cube Root of Unity
  6. 6If and , then the area of the triangle whose vertices are is2025Cube Root of Unity
  7. 7If and be two roots of the equation , then the origin, and form an equilateral triangle if2024Geometry of Complex Number
  8. 8If , is the root of the equation then the value of is2024Polar and Euler Form
  9. 9If the vertices of a square are \(z_1, z_2, z_3\) and \(z_4\) taken in the anti-clockwise order, then \(z_3=\)2023Geometry of Complex Number
  10. 10Reflection of the line \( {a} z+a {z}=0\) in the real axis is given by2023Geometry of Complex Number
  11. 11If \(z_1\) and \(z_2\) are two complex numbers satisfying the equation \( | {z_1+z_2}{z_1-z_2} |=1\), then \( {z_1}{z_2}\) may be2023Geometry of Complex Number
  12. 12If , then Maximum Minimum is equal to2022Conjugate, modulus and argument
  13. 13If - iy and iq , then is equal to2022Algebra of complex numbers
  14. 14The side of is fixed and is of length unit. The vertex moves in the plane such that the vertical angle is always constant and is . Let -axis2022Geometry of Complex Number
  15. 15Let and be two non-zero complex numbers. Then2022Conjugate, modulus and argument
  16. 16Let denote the set of all complex numbers. Define and and . Then2021Conjugate, modulus and argument
  17. 17If and , then all the points representing lie on;2021De Moivres Theorem
  18. 18If for a complex number , then2021Geometry of Complex Number
  19. 19The number of complex numbers such that and imaginary part of is 0, is2020Conjugate, modulus and argument
  20. 20The equation represents a circle of radius2020Geometry of Complex Number
  21. 21Let and be two imaginary roots of , where and are real. The points and origin form an equilateral triangle if2020Locus Based on Distance Formula
  22. 22Let be a complex number such that the principal value of argument, arg Then, arg is2019Conjugate, modulus and argument
  23. 23The general value of the real angle , which satisfies the equation. is given by, (assuming is an integer)2019Polar and Euler Form
  24. 24For any non-zero complex number , the minimum value of is2019Conjugate, modulus and argument
  25. 25The polar coordinate of a point is The polar coordinate of the point which is such that line joining is bisected perpendicularly by the init2019Polar and Euler Form
  26. 26If and is real number, then will be (when Set of integers)2019Conjugate, modulus and argument
  27. 27If then is equal to2018De Moivres Theorem
  28. 28If and be two non-zero complex numbers such that then the origin and the points represented by and2018Locus Based on Distance Formula
  29. 29Let and be complex numbers such that and If and then is2018Conjugate, modulus and argument
  30. 30The expression equals2017Power of iota
  31. 31Let where and are real. The points in the plane for which is purely imaginary, lie on2017Conjugate, modulus and argument
  32. 32Let and be the roots of If be a positive integer, then is2017Polar and Euler Form
  33. 33The complex number satisfying the equation is2017Locus Based on Distance Formula
  34. 34The value of is2016Power of iota
  35. 35If are imaginary numbers such that then is2016Conjugate, modulus and argument
  36. 36equals2016De Moivres Theorem
  37. 37If then for any integer2016Polar and Euler Form
  38. 38The value of is2015Cube Root of Unity
  39. 39Find the maximum value of when where being a complex number.2015Conjugate, modulus and argument
  40. 40The value of is minimum when equals2014Conjugate, modulus and argument
  41. 41Let be two fixed complex numbers in the argand plane and be an arbitrary point satisfying . Then, the locus of will be2014Locus Based on Distance Formula
  42. 42Let be a fixed point on the circle of radius 1 centred at the origin in the argand plane and Consider an equilateral triangle inscribed in t2014Polar and Euler Form
  43. 43Suppose that are three vertices of an equilateral triangle in the angand plane. Let and be a non-zero complex number. The points will be2014Rotation Theorem
  44. 44In the argand plane, the distinct roots of is a complex number) represent vertices of2014Polar and Euler Form
  45. 45Let denote the cube roots of unity other than 1 and Let Then the value of is2014Cube Root of Unity
  46. 46If and be two points on the complex plane. Then, the set of complex number satisfying represents2013Conjugate, modulus and argument
  47. 47If and are roots of then the value of is2013Cube Root of Unity
  48. 48If where and are real numbers and , then the points for which is real, lie on2013Geometry of Complex Number
  49. 49If and are angles of an isosceles triangle and then the value of2013Polar and Euler Form
  50. 50The maximum value of , when the complex number satisfies the condition is2012Conjugate, modulus and argument

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 59 questions compiled from WBJEE papers spanning 2009 to 2026.

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

These are WBJEE 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 WBJEE Mathematics?

Complex Number has appeared in 18 of the 18 years of WBJEE papers covered here, with 59 questions across 18 papers - about 3 per paper it appears in.

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

Of the 59 questions analysed for this chapter, 27% are easy, 54% moderate and 19% tough. 2014 had the most, with 6 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 - 20 questions (34%)
  • Polar and Euler Form - 9 questions (15%)
  • Geometry of Complex Number - 9 questions (15%)
  • Geometry of Complex Number has produced the most tough questions (5).
6.Is Complex Number's weightage in WBJEE going up or down?

Across all 18 papers analysed, Complex Number has averaged about 3.3 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.7 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.