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Mathematics - Complex Number

Practise 39 JEE Advanced previous year questions on Complex Number, compiled from papers spanning 2006 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Advanced tests.

Complex Number has been asked in 20 of the 27 years of JEE Advanced papers analysed (2000–2026), with 39 questions in all. 15% of them were easy, 44% moderate and 41% tough. Most of its questions came from 2008, with 4 questions that year. In the last three years (2024–2026) it had 3 questions across 6 papers, about 0.5 per paper.

The chapter's 8 topics are not weighted equally: Conjugate, modulus and argument (10 questions, 26%), Algebra of complex numbers (9 questions, 23%), and Geometry of Complex Number (8 questions, 21%) have been asked the most. Over the last five years the most frequent topics have been Algebra of complex numbers (3), Conjugate, modulus and argument (2), and Polar and Euler Form (1). Conjugate, modulus and argument has produced the most tough questions (5).

  1. 1Let denote the set of all real numbers. Let and be two complex numbers, where . Let . Then which of the following statements is (are) TRUE?2025 (Paper 1)Locus Based on Distance Formula
  2. 2For a non-zero complex number , let denote the principal argument of , with . Let be the cube root of unity for which . Let . Then the value2025 (Paper 2)Cube Root of Unity
  3. 3Let , and . Then which of the following statements is (are) TRUE?2024 (Paper 1)Polar and Euler Form
  4. 4Let A = 1967 + 1686 i sin 7 - 3 i cos : R . If A contains exactly one positive integer n , then the value of n is2023 (Paper 1)Algebra of complex numbers
  5. 5Let z be a complex number satisfying z 3 + 2 z 2 + 4 z - 8 = 0 , where z denotes the complex conjugate of z . Let the imaginary part of z be2023 (Paper 1)Algebra of complex numbers
  6. 6Let A 1 , A 2 , A 3 , , A 8 be the vertices of a regular octagon that lie on a circle of radius 2 . Let P be a point on the circle and let P2023 (Paper 2)nth roots of unity
  7. 7Let z be a complex number with non-zero imaginary part. If 2 + 3 z + 4 z 2 2 - 3 z + 4 z 2 is a real number, then the value of z 2 is ______2022 (Paper 1)Conjugate, modulus and argument
  8. 8Let z denote the complex conjugate of a complex number z and let i = - 1 . In the set of complex numbers, the number of distinct roots of th2022 (Paper 1)Algebra of complex numbers
  9. 9Let z denote the complex conjugate of a complex number z . If z is a non-zero complex number for which both real and imaginary parts of z 2 2022 (Paper 2)Conjugate, modulus and argument
  10. 10Let 1 , 2 , , 10 be positive valued angles (in radian) such that 1 + 2 + + 10 = 2 . Define the complex numbers z 1 = e i 1 , z k = z k - 1 e2021 (Paper 1)Conjugate, modulus and argument
  11. 11For any complex number w = c + i d , let arg w ( - , ] , where i = - 1 . Let and be real numbers such that for all complex numbers z = x + i2021 (Paper 1)Geometry of Complex Number
  12. 12Let S be the set of all complex numbers z satisfying z 2 + z + 1 = 1 . Then which of the following statements is/are TRUE?2020 (Paper 1)Polar and Euler Form
  13. 13For a complex number z , let Re z denote the real part of z . Let S be the set of all complex numbers z satisfying z 4 - | z | 4 = 4 i z 2 ,2020 (Paper 2)Conjugate, modulus and argument
  14. 14Let S be the set of all complex numbers z satisfying z - 2 + i 5 . If the complex number z 0 is such that 1 z 0 - 1 is the maximum of the se2019 (Paper 1)Geometry of Complex Number
  15. 15Let 1 be a cube root of unity. Then the minimum of the set { a + b + c 2 2 : a , b , c distinct non zero integers } equals ________2019 (Paper 1)Cube Root of Unity
  16. 16For a non-zero complex number z , let arg ( z ) denote the principal argument with - a r g z then, which of the following statement(s) is (a2018 (Paper 1)Conjugate, modulus and argument
  17. 17Let s , t , r be non-zero complex numbers and L be the set of solutions z = x + i y x , y , i = - 1 of the equation s z + t z - + r = 0 , wh2018 (Paper 2)Conjugate, modulus and argument
  18. 18Let a , b , x and y be real numbers such that a - b = 1 and y 0 . If the complex number z = x + i y satisfies I m a z + b z + 1 = y , then w2017 (Paper 1)Algebra of complex numbers
  19. 19Let a , b R and a 2 + b 2 0 . Suppose S = z C : z = 1 a + i b t , t R , t 0 , where i = - 1 . If z = x + i y and z S , then x , y lies on2016 (Paper 2)Geometry of Complex Number
  20. 20For any integer k , let k = cos k 7 + i sin k 7 , w h e r e i = - 1 . The value of the expression k = 1 12 k + 1 - k k = 1 3 4 k - 1 - 4 k -2015 (Paper 2)nth roots of unity
  21. 21Let z k = cos 2 k 10 + i sin 2 k 10 ; k = 1 , 2 , , 9 List I List II (A) For each z k there exists a z j s u c h z k . z j = 1 (P) True (B) 2014 (Paper 2)nth roots of unity
  22. 22Let complex numbers and 1 lie on circles x - x 0 2 + y - y 0 2 = r 2 , and x - x 0 2 + y - y 0 2 = 4 r 2 , respectively. If z 0 = x 0 + i y 2013 (Paper 1)Geometry of Complex Number
  23. 23Let w = 3 + i 2 and P = w n : n = 1, 2, 3, .Further H 1 = z C : Re z 1 2 and H 2 = z C : Re z - 1 2 , where C is the set of all complex numb2013 (Paper 2)Geometry of Complex Number
  24. 24Let be a complex number such that the imaginary part of is non-zero and is real. Then a cannot take the value2012 (Paper 1)Algebra of complex numbers
  25. 25Paragraph: Let , b and be three real numbers satisfying Question: Let be a solution of with . If , with and satisfying Eq. (E), then the val2011 (Paper 1)Cube Root of Unity
  26. 26If is any complex number satisfying , then the maximum value of is2011 (Paper 1)Conjugate, modulus and argument
  27. 27Let and be non-zero complex numbers such that . Then, the value of is2011 (Paper 2)Cube Root of Unity
  28. 28Let and be two distinct complex numbers and let for some real number with . If denotes the principal argument of a non-zero complex number ,2010 (Paper 1)Conjugate, modulus and argument
  29. 29Let be the complex number . Then the number of distinct complex number satisfying is equal to2010 (Paper 1)Conjugate, modulus and argument
  30. 30Match the statements of Column I with these in Column II. [Note : Here takes values in the complex plane and and denote respectively, the im2010 (Paper 2)Algebra of complex numbers
  31. 31Let . Then, the value of at is2009 (Paper 1)Polar and Euler Form
  32. 32Let be a complex number, where and are integers. Then, the area of the rectangle whose vertices are the roots of the equation is2009 (Paper 1)Algebra of complex numbers
  33. 33Paragraph: Let be three sets of complex numbers as defined below. . Question: The number of elements in the set is2008 (Paper 1)Geometry of Complex Number
  34. 34Paragraph: Let be three sets of complex numbers as defined below. . Question: Let be any point in . The lies between2008 (Paper 1)Algebra of complex numbers
  35. 35Paragraph: Let be three sets of complex numbers as defined below. . Question: Let be any point in and let be any point satisfying . Then, li2008 (Paper 1)Algebra of complex numbers
  36. 36A particle starts from the point , where . It moves first horizontally away from origin by 5 units and then vertically away from origin by 32008 (Paper 2)Rotation Theorem
  37. 37A man walks a distance of 3 units from the origin towards the North-East direction. From there, he walks a distance of 4 units towards the N2007 (Paper 1)Geometry of Complex Number
  38. 38If and , then all the values of lie on2007 (Paper 2)Geometry of Complex Number
  39. 39If , where and satisfies the condition that is purely real, then the set of values of is2006Conjugate, modulus and argument

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 39 questions compiled from JEE Advanced papers spanning 2006 to 2025.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Complex Number has appeared in 20 of the 21 years of JEE Advanced papers covered here, with 39 questions across 30 papers - about one per paper it appears in.

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

Of the 39 questions analysed for this chapter, 15% are easy, 44% moderate and 41% tough. 2008 had the most, with 4 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 - 10 questions (26%)
  • Algebra of complex numbers - 9 questions (23%)
  • Geometry of Complex Number - 8 questions (21%)
  • Conjugate, modulus and argument has produced the most tough questions (5).
6.Is Complex Number's weightage in JEE Advanced going up or down?

Across all 30 papers analysed, Complex Number has averaged about 1.3 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.