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Previous year question hub

Complex Numbers - Algebra - Mathematics Previous Year Questions

Practice Complex Numbers - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

51Papers
42Years
84Questions
1Topics

Complex Numbers question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Complex Numbers. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 46 54.8%
Easy 26 31%
Hard 8 9.5%
Not classified 4 4.8%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 60 71.4%
Subjective 15 17.9%
Numerical Answer Type (NAT) 9 10.7%

Subject weightage

Top subjects by unique question coverage.

Mathematics
84 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
84 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Complex Numbers
84 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE ADVANCED 2025 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2022 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
2 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2014 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 2 OFFLINE
3 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 2 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
2 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 1 OFFLINE
2 Qs
IIT JEE 2008 PAPER 1 OFFLINE
3 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
1 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
2 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003
2 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002
2 Qs
IIT JEE 2002 SCREENING
1 Qs
IIT JEE 2001 SCREENING
2 Qs
IIT JEE 2000 SCREENING
2 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
3 Qs
IIT JEE 1997
1 Qs
IIT JEE 1996
1 Qs
IIT JEE 1995 SCREENING
3 Qs
IIT JEE 1995
2 Qs
IIT JEE 1992
1 Qs
IIT JEE 1990
1 Qs
IIT JEE 1988
1 Qs
IIT JEE 1987
2 Qs
IIT JEE 1986
2 Qs
IIT JEE 1985
3 Qs
IIT JEE 1984
2 Qs
IIT JEE 1983
3 Qs
IIT JEE 1982
2 Qs
IIT JEE 1981
3 Qs
IIT JEE 1980
2 Qs
IIT JEE 1979
2 Qs
IIT JEE 1978
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE ADVANCED 2025 PAPER 1 ONLINE20251View paper
JEE ADVANCED 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 1 ONLINE20242View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20232View paper
JEE ADVANCED 2022 PAPER 1 ONLINE20222View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20212View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20171View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
JEE ADVANCED 2014 PAPER 2 OFFLINE20141View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
JEE ADVANCED 2013 PAPER 2 OFFLINE20133View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2011 PAPER 2 OFFLINE20111View paper
IIT JEE 2010 PAPER 1 OFFLINE20102View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 1 OFFLINE20092View paper
IIT JEE 2008 PAPER 1 OFFLINE20083View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 1 OFFLINE20071View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200620062View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 200320032View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 200220022View paper
IIT JEE 2002 SCREENING20021View paper
IIT JEE 2001 SCREENING20012View paper
IIT JEE 2000 SCREENING20002View paper
IIT JEE 199919992View paper
IIT JEE 199819983View paper
IIT JEE 199719971View paper
IIT JEE 199619961View paper
IIT JEE 199519952View paper
IIT JEE 1995 SCREENING19953View paper
IIT JEE 199219921View paper
IIT JEE 199019901View paper
IIT JEE 198819881View paper
IIT JEE 198719872View paper
IIT JEE 198619862View paper
IIT JEE 198519853View paper
IIT JEE 198419842View paper
IIT JEE 198319833View paper
IIT JEE 198219822View paper
IIT JEE 198119813View paper
IIT JEE 198019802View paper
IIT JEE 197919792View paper
IIT JEE 197819781View paper

All Complex Numbers previous year questions

Practice every matching question in batches of 20, with every available option.

1
1978 · Mathematics · Algebra · Complex Numbers
IIT JEE 1978
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 = \({a^3} + {b^3}\).
Write your response
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2
1979 · Mathematics · Algebra · Complex Numbers
IIT JEE 1979
If x + iy = \(\sqrt {{{a + ib} \over {c + id}}}\), prove that \({({x^2} + {y^2})^2} = {{{a^2} + {b^2}} \over {{c^2} + {d^2}}}\).
Write your response
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3
1979 · Mathematics · Algebra · Complex Numbers
IIT JEE 1979
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
A
\(- 1,1 + 2\omega ,\,1 + 2{\omega ^2}\)
B
\(- 1,1 - 2\omega ,\,1 - 2{\omega ^2}\)
C
\(- 1, - 1, - 1\)
D
None of these
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4
1980 · Mathematics · Algebra · Complex Numbers
IIT JEE 1980
Find the real values of x and y for which the following equation is satisfied \(\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i\)
Write your response
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5
1980 · Mathematics · Algebra · Complex Numbers
IIT JEE 1980
The smallest positive integer n for which \({\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1\) is
A
\(n = 8\)
B
\(n = 16\)
C
\(n = 12\)
D
none of these
Open complete paper
6
1981 · Mathematics · Algebra · Complex Numbers
IIT JEE 1981
For complex number \({z_1} = {x_1} + i{y_1}\) and \({z_2} = {x_2} + i{y_2},\) we write \({z_1} \cap {z_2},\,\,if\,\,{x_1} \le {x_2}\,\,and\,\,{y_1} \le {y_2}.\)
Then for all complex numbers \(z\,\,with\,\,1 \cap z,\) we have \({{1 - z} \over {1 + z}} \cap 0.\)
A
TRUE
B
FALSE
Open complete paper
7
1981 · Mathematics · Algebra · Complex Numbers
IIT JEE 1981
Let the complex number \({{z_1}}\), \({{z_2}}\) and \({{z_3}}\) be the vertices of an equilateral triangle. Let \({{z_0}}\) be the circumcentre of the triangle. Then prove that \(z_1^2 + z_2^2 + z_3^2 = 3z_0^2\).
Write your response
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8
1981 · Mathematics · Algebra · Complex Numbers
IIT JEE 1981
The complex numbers \(z = x + iy\) which satisfy the equation \(\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1\) lie on
A
the x-axis
B
the straight line y=5
C
a circle passing through the origin
D
none of these
Open complete paper
9
1982 · Mathematics · Algebra · Complex Numbers
IIT JEE 1982
If \(z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5},\) then
A
\({\mathop{\rm Re}\nolimits} \left( z \right) = 0\)
B
\({\rm I}m\left( z \right) = 0\)
C
\({\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) > 0\,\)
D
\({\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) < 0\)
Open complete paper
10
1982 · Mathematics · Algebra · Complex Numbers
IIT JEE 1982
The inequality |z-4| < |z-2| represents the region given by
A
\({\mathop{\rm Re}\nolimits} \left( z \right) \ge 0\,\,\)
B
\({\mathop{\rm Re}\nolimits} \left( z \right) < 0\)
C
\({\mathop{\rm Re}\nolimits} \left( z \right) > 0\)
D
none of these
Open complete paper
11
1983 · Mathematics · Algebra · Complex Numbers
IIT JEE 1983
If \(z = x + iy\) and \(\omega = \left( {1 - iz} \right)/\left( {z - i} \right),\) then \(\,\left| \omega \right| = 1\) implies that, in the complex plane,
A
\(z\) lies on the imaginary axis
B
\(z\) lies on the real axis
C
\(z\) lies on the unit circle
D
none of these
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12
1983 · Mathematics · Algebra · Complex Numbers
IIT JEE 1983
Prove that the complex numbers \({{z_1}}\), \({{z_2}}\) and the origin form an equilateral triangle only if \(z_1^2 + z_2^2 - {z_1}\,{z_2} = 0\).
Write your response
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13
1983 · Mathematics · Algebra · Complex Numbers
IIT JEE 1983
The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if
A
z1 + z4 = z2 + z3
B
z1 + z3 = z2 + z4
C
z1 + z2 = z3 + z4
D
None of these
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14
1984 · Mathematics · Algebra · Complex Numbers
IIT JEE 1984
If the complex numbers, \({Z_1},{Z_2}\) and \({Z_3}\) represent the vertics of an equilateral triangle such that
\(\left| {{Z_1}} \right| = \left| {{Z_2}} \right| = \left| {{Z_3}} \right|\) then \({Z_1} + {Z_2} + {Z_3} = 0.\)
A
TRUE
B
FALSE
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15
1984 · Mathematics · Algebra · Complex Numbers
IIT JEE 1984
If 1, \({{a_1}}\), \({{a_2}}\)......,\({a_{n - 1}}\) are the n roots of unity, then show that (1- \({{a_1}}\)) (1- \({{a_2}}\)) (1- \({{a_3}}\)) ....\((1 - \,a{ - _{n - 1}}) = n\)
Write your response
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16
1985 · Mathematics · Algebra · Complex Numbers
IIT JEE 1985
If three complex numbers are in A.P. then they lie on a circle in the complex plane.
A
TRUE
B
FALSE
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17
1985 · Mathematics · Algebra · Complex Numbers
IIT JEE 1985
If \({z_1}\) = a + ib and \({z_2}\) = c + id are complex numbers such that \(\left| {{z_1}} \right| = \left| {{z_2}} \right| = 1\) and \({\mathop{\rm Re}\nolimits} ({z_1}\,{\overline z _2}) = 0\), then the pair of complex numbers \({w_1}\) = a + ic and \({w_2}\) = b+ id satisfies -
A
\(\left| {{w_1}} \right| = 1\,\)
B
\(\left| {{w_2}} \right| = 1\,\)
C
\({\mathop{\rm Re}\nolimits} ({w_1}\,{\overline w _2}) = 0\)
D
none of these
Open complete paper
18
1985 · Mathematics · Algebra · Complex Numbers
IIT JEE 1985
If \(a,\,b,\,c\) and \(u,\,v,\,w\) are complex numbers representing the vertics of two triangles such that \(c = \left( {1 - r} \right)a + rb\) and \(w = \left( {1 - r} \right)u + rv,\) where \(w = \left( {1 - r} \right)u + rv,\) is a complex number, then the two triangles
A
have the same area
B
are similar
C
are congruent
D
none of these
Open complete paper
19
1986 · Mathematics · Algebra · Complex Numbers
IIT JEE 1986
Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z + iz is \({1 \over 2}\,{\left| z \right|^2}\) .
Write your response
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20
1986 · Mathematics · Algebra · Complex Numbers
IIT JEE 1986
Let \({z_1}\) and \({z_2}\) be complex numbers such that \({z_1}\) \(\ne\) \({z_2}\) and \(\left| {{z_1}} \right| =\,\left| {{z_2}} \right|\). If \({z_1}\) has positive real and \({z_2}\) has negative imaginary part, then \({{{z_1}\, + \,{z_2}} \over {{z_1}\, - \,{z_2}}}\) may be
A
zero
B
real and positive
C
real and negative
D
purely imaginary
Open complete paper

Showing 20 of 84 questions