Complex Numbers
JEE Advanced / Mathematics / Algebra / 106 questions
MathematicsAlgebra106 PYQs
Practice 106 JEE Advanced Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
106
PYQs on Page
Mathematics / Algebra
1978-2026
Year Range
Based on indexed question metadata
12
Last 5 Years
2022-2026
21
Last 10 Years
2017-2026
Recent Year Trend
2021
2022
2023
2024
2025
2026Latest year
20213 max PYQs/year2026
Question Types
106PYQs
MCQ43.4%
MCQM18.9%
SUBJECTIVE17.9%
INTEGER10.4%
FILL-BLANKS5.7%
T/F3.8%
Difficulty Mix
#1 Medium61
#2 Easy27
#3 Hard13
#4 Unknown5
12 in last 5 years21 in last 10 years
Complex Numbers Questions
Showing 6 of 106 questions on this page.
1Complex Numbers
Find the real values of x and y for which the following equation is satisfied \(\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i\)
SUBJECTIVE+2 / -01980
2Complex Numbers
The smallest positive integer n for which \({\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1\) is
MCQ+2 / -0.51980
3Complex Numbers
If the cube roots of unity are \(1,\,\omega ,\,{\omega ^2},\) then the roots of the equation \({\left( {x - 1} \right)^3} + 8 = 0\) are
MCQ+2 / -0.51979
4Complex Numbers
If x + iy = \(\sqrt {{{a + ib} \over {c + id}}}\), prove that \({({x^2} + {y^2})^2} = {{{a^2} + {b^2}} \over {{c^2} + {d^2}}}\).
SUBJECTIVE+2 / -01979
5Complex Numbers
Express \({1 \over {1 - \cos \,\theta + 2i\sin \theta }}\) in the form x + iy.
SUBJECTIVE+2 / -01978
6Complex Numbers
If x = a + b, y = a\(\gamma\) + b\(\beta\) and z = a\(\beta\) +b\(\gamma\) where \(\gamma\) and \(\beta\) are the complex cube roots of unity, show that xyz = \({a^3} + {b^3}\).
SUBJECTIVE+2 / -01978
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