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Mathematics - Complex Number

Practise 108 NTA Abhyas (JEE Main) questions on Complex Number. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Complex Number has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 108 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1If λ ∈ R such that the origin and the non-real roots of the equation 2 z 2 + 2 z + λ = 0 form the vertices of an equilateral triangle in the
  2. 2If α , β ∈ C are the distinct roots of the equation x 2 - x + 1 = 0 , then α 101 + β 107 is equal to
  3. 3The solution of the equation z - z = 1 + 2 i is
  4. 4For a complex number z , the product of the real parts of the roots of the equation z 2 - z = 5 - 5 i is (where, i = - 1 )
  5. 5If x 4 + 2 x i - 3 x 2 + y i = 3 - 5 i + 1 + 2 y i , then the number of ordered pairs x , y is/are equal to x , y R a n d i 2 = - 1
  6. 6For the complex number Z , the sum of all the solutions of Z 2 + Z = Z 2 is equal to
  7. 7For the equation 1 - i x 1 + i x = s i n π 7 - i c o s π 7 , if x = c o t k π 28 , then the value of k can be (where i 2 = - 1 )
  8. 8If Im i z + 2 z + i = - 1 represents part of a circle with radius r units, then the value of 4 r 2 is (where, z C , z i , Im z represents th
  9. 9The real part of the complex number z satisfying z - 1 - 2 i ≤ 1 and having the least positive argument, is
  10. 10The number of solutions of the equation z 3 + 3 z ¯ 2 z = 0 (where, z is a complex number) are
  11. 11Let Z = x + i y is a complex number, such that x 2 + y 2 = 1 . In which of the following cases Z 1 - Z for x ≠ 1 lies in the Ι Ι n d quadran
  12. 12If z = x + i y , ∀ x , y ∈ R , i 2 = - 1 , x y ≠ 0 and z = 2 , then the imaginary part of z + 2 z - 2 cannot be
  13. 13If z = 3 − 4 i , then the value of expression z 4 − 3 z 3 + 3 z 2 + 99 z − 95 is equal to
  14. 14If the cubic equation z 3 + a z 2 + b z + c = 0 a , b , c R , c 0 has a purely imaginary root, then (where i 2 = - 1 )
  15. 15If a and b are two real numbers lying between 0 and 1 , such that Z 1 = a + i , Z 2 = 1 + b i and Z 3 = 0 form an equilateral triangle, then
  16. 16Let Z = r e i θ ( r 0 and π θ ≤ 3 π ) is a root of the equation Z 8 - Z 7 + Z 6 - Z 5 + Z 4 - Z 3 + Z 2 - Z + 1 = 0 . If the sum of all valu
  17. 17If z 1 , z 2 and z 3 are three complex numbers such that z 1 = z 2 = z 3 = 1 z 1 + 1 z 2 + 1 z 3 = 1 , then z 1 + z 2 + z 3 is
  18. 18z ∈ C satisfies the condition z ≥ 3 . Then the least value of z + 1 z is
  19. 19Let α and β be the roots of the equation x 2 + 2 x + 2 = 0 , then α 15 + β 15 is equal to
  20. 20If Z - 2 = 2 Z - 1 , then the value of R e Z Z 2 is (where Z is a complex number and Re( Z ) represents the real part of Z )
  21. 21The complex number z , satisfying the equation z 3 = z - and arg z + 1 = 4 simultaneously, is (where, i 2 = - 1 )
  22. 22If x + 1 x = 1 , = x 4 0 0 0 + 1 x 4 0 0 0 and be the digit at the unit place of the number 2 2 n + 1 , where n N and n 1 , then the value o
  23. 23Let the points A , B , C and D are represented by complex numbers Z 1 , Z 2 , Z 3 and Z 4 respectively. If A , B and C are not collinear and
  24. 24If the arguments of 1 - i 3 + i 1 + 3 i and Z - 2 Z ¯ - 1 are equal, then the locus of Z is part of a circle with centre a , b . The value o
  25. 25Let Z be a complex number satisfying the relation Z 3 + 4 Z 2 Z = 0 . If the least possible argument of Z is k , then k is equal to (here, a
  26. 26If z is a complex number, then the area of the triangle (in sq. units) whose vertices are the roots of the equation z 3 + i z 2 + 2 i = 0 is
  27. 27For a complex number Z , if the argument of Z - a Z ¯ - b is π 4 or - 3 π 4 (where a , b are two real numbers), then the value of a b such t
  28. 28The value of k = 1 99 i k ! + k ! is (where, i = - 1 and is non-real cube root of unity)
  29. 29For a complex number Z , if arg Z - , , then arg 1 + cos 6 7 + i sin 6 7 is (here i 2 = - 1 )
  30. 30Let z 1 = 1 , z 2 = 2 , z 3 = 3 and z 1 + z 2 + z 3 = 3 + 5 i , then the value of Re z 1 z 2 - + z 2 z 3 - + z 3 z 1 - is equal to (Where z
  31. 31For the complex number z satisfying the condition z + 2 z = 2 , the maximum value of z is
  32. 32Two points P and Q in the argand plane represent the complex numbers z and 3 z + 2 + i . If z = 2 , then Q moves on the circle, whose centre
  33. 33If i 2 = - 1 and 1 + i 2 n = 1 - i 2 m = 1 , n , m N , then the minimum value of n + m is equal to
  34. 34An insect starts from the origin in the argand plane and goes 4 k m ( N 45 E ) then it moves 3 k m N 45 W and then takes an angular movement
  35. 35If z is a non-real complex number, then the minimum value of I m z 5 I m z 5 is ( I m z = Imaginary part of z )
  36. 36If z 1 , z 2 and z 3 are the vertices of a triangle in the argand plane such that z 1 - z 2 = z 1 - z 3 , then arg ⁡ 2 z 1 - z 2 - z 3 z 3 -
  37. 37If a and b are positive integers such that N = a + i b 3 - 107 i (where N is a natural number), then the value of a is equal to (where i 2 =
  38. 38If Z = cos ⁡ ϕ + i sin ⁡ ϕ ∀ ϕ ∈ π 3 , π , then the value of arg Z 2 - Z is equal to (where, arg ( Z ) represents the argument of the comple
  39. 39If 4 i 3 - i 2 i + 1 2 = r cos + i sin , then cos + sin is equal to (where, i 2 = - 1 )
  40. 40If the origin and the non-real roots of the equation 3 z 2 + 3 z + λ = 0 , ∀ λ ∈ R are the vertices of an equilateral triangle in the argand
  41. 41For a complex number Z , if the argument of 3 + 3 i and Z - 2 Z - - 1 are equal, then the maximum distance of Z from the x -axis is equal to
  42. 42The value of ∑ k = 1 10 sin ⁡ 2 π k 11 - i cos ⁡ 2 π k 11 is (where i = - 1 )
  43. 43If z 1 , z 2 and z 3 are 3 distinct complex numbers such that 3 z 1 - z 2 = 5 z 2 - z 3 = 7 z 3 - z 1 , then the value of 9 z 1 - z 2 + 25 z
  44. 44For a complex number Z , if Z = π 4 1 + i 4 1 - π i π + i + π - i 1 + π i , then the value of Z amp Z is equal to (where amp Z ∈ - π , π )
  45. 45A complex number z is said to be unimodular if | z | = 1 . Let, z 1 and z 2 are complex numbers such that z 1 - 2z 2 2 - z 1 z ¯ 2 is unimod
  46. 46For a complex number Z , if Z - i ≤ 2 and Z 1 = 5 + 3 i , then the maximum value of i Z + Z 1 is (where, i 2 = - 1 )
  47. 47Let z 1 = 3 , z 2 = 2 and z 1 + z 2 + z 3 = 3 + 4 i . If the real part of z 1 z 2 - + z 2 z 3 - + z 3 z 1 - is equal to 4 , then z 3 is equa
  48. 48If equation Z - 1 n = Z n = 1 ∀ n ∈ N has solutions, then n can be
  49. 49For a complex number z , the equation z 2 + p + i q z + r + i s = 0 has a real root (where p , q , r , s are non-zero real numbers and i 2 =
  50. 50Let z = x + i y and w = u + i v be two complex numbers, such that z = w = 1 and z 2 + w 2 = 1 . Then, the number of ordered pairs z , w is e

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 108 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Complex Number questions in NTA Abhyas (JEE Main)?

Of the 108 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

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

All of this chapter's questions come from a single topic: Uncategorized.