Jump to a section

Mathematics - Complex Number

Practise 37 KCET previous year questions on Complex Number, compiled from papers spanning 2007 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 KCET tests.

Complex Number has been asked in 19 of the 20 years of KCET papers analysed (2007–2026), with 37 questions in all. 59% of them were easy, 30% moderate and 11% tough. Most of its questions came from 2011, with 5 questions that year. In the last three years (2024–2026) it had 3 questions across 3 papers, about 1 per paper.

The chapter's 8 topics are not weighted equally: Conjugate, modulus and argument (12 questions, 32%), Cube Root of Unity (7 questions, 19%), and Algebra of complex numbers (7 questions, 19%) have been asked the most. Conjugate, modulus and argument has also led over the last five years, with 2 questions. nth roots of unity has produced the most tough questions (2).

  1. 1Preview not available - open to view this question.2026Power of iota
  2. 2If and are two non-zero complex numbers, then which of the following is not true?2025Conjugate, modulus and argument
  3. 3The real value of ' ' for which is purely real is2024Algebra of complex numbers
  4. 4The modulus of the complex number is2023Conjugate, modulus and argument
  5. 5If where and are real numbers, then the values of and are respectively,2022Algebra of complex numbers
  6. 6If , then2021Algebra of complex numbers
  7. 7The value of is2020Geometry of Complex Number
  8. 8If \( ( {1-i}{1+i} )^{96}=a+i b \) then \( (a, b) \) is2018Power of iota
  9. 9If \( y= ^{-1} ( { x+ x}{ x- x} ) \), then \( {d y}{d x} \) is equal to2017Power of iota
  10. 10The real part of \( (1- +i )^{-1} \) is2016Algebra of complex numbers
  11. 11The simplified form of \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3} \) is2016Power of iota
  12. 12If the eccentricity of the hyperbola \( {x^{2}}{a^{2}}- {y^{2}}{b^{2}}=1 \) is \( {5}{4} \) and \( 2 x+3 y-6=0 \) is a focal chord of the hy2015Conjugate, modulus and argument
  13. 13The function \( f(x)=[x] \), where \( [x] \) denotes greatest integer function is continuous at2015Cube Root of Unity
  14. 14If \( y=(1+x) (1+x^{2} ) (1+x^{4} ) \), then \( {d y}{d x} \) at \( x=1 \) is2014Conjugate, modulus and argument
  15. 15The modulus and amplitude of are2013Conjugate, modulus and argument
  16. 16If , then the value of is2013Cube Root of Unity
  17. 17The number of solutions of the equation , where , are2012Conjugate, modulus and argument
  18. 18If is a complex number such that , then is equal to2012nth roots of unity
  19. 19If the conjugate of is , then2012Conjugate, modulus and argument
  20. 20If and are different complex numbers with , then is equal to2012Conjugate, modulus and argument
  21. 21If is an imaginary cube root of unity, then the value of is2011Cube Root of Unity
  22. 22The value of is2011Algebra of complex numbers
  23. 23If is an imaginary cube root of unity, then the value of (2n factors) is2011Cube Root of Unity
  24. 24If denotes in Argand's plane and , then the locus of is a/an2011Locus Based on Distance Formula
  25. 25In Argand's plane, the point corresponding to lies in2011Algebra of complex numbers
  26. 26The least positive integer , for which is positive, is2010Power of iota
  27. 27If , then is2010Cube Root of Unity
  28. 28The smallest positive integral value of such that is equal to2009Conjugate, modulus and argument
  29. 29The complex number lies in2009Algebra of complex numbers
  30. 30If is the point in the Agrand diagram corresponding to the complex number and if is an isosceles right angled triangle, right angled at ' ',2009Geometry of Complex Number
  31. 31If is a complex number satisfying the equation , then is equal to2008Cube Root of Unity
  32. 32If is a complex number such that , then2008Conjugate, modulus and argument
  33. 33The value of is2008nth roots of unity
  34. 34The conjugate of the complex number is2007Conjugate, modulus and argument
  35. 35The imaginary part of is2007Polar and Euler Form
  36. 36The amplitude of is2007Conjugate, modulus and argument
  37. 37If are the cube roots of unity, then is equal to2007Cube Root of Unity

Frequently Asked Questions

1.How many questions are available for Complex Number?

This chapter includes 37 questions compiled from KCET papers spanning 2007 to 2026.

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

These are KCET 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 KCET Mathematics?

Complex Number has appeared in 19 of the 20 years of KCET papers covered here, with 37 questions across 19 papers - about 2 per paper it appears in.

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

Of the 37 questions analysed for this chapter, 59% are easy, 30% moderate and 11% tough. 2011 had the most, with 5 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 - 12 questions (32%)
  • Cube Root of Unity - 7 questions (19%)
  • Algebra of complex numbers - 7 questions (19%)
  • nth roots of unity has produced the most tough questions (2).
6.Is Complex Number's weightage in KCET going up or down?

Across all 19 papers analysed, Complex Number has averaged about 1.9 questions per paper. In the last three years (2024–2026), that average has fallen, 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.