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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.

15Papers
14Years
48Questions
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.

Not classified 48 100%

Question type distribution

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

Multiple Choices 47 97.9%
Subjective 1 2.1%

Subject weightage

Top subjects by unique question coverage.

Mathematics
48 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
48 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Complex Numbers
48 Qs

Paper coverage

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

WB JEE 2025
3 Qs
VITEEE 2025
2 Qs
WB JEE 2024
2 Qs
WB JEE 2023
3 Qs
WB JEE 2022
3 Qs
WB JEE 2021
3 Qs
WB JEE 2020
2 Qs
WB JEE 2019
5 Qs
WB JEE 2018
4 Qs
WB JEE 2017
3 Qs
WB JEE 2016
3 Qs
WB JEE 2011
3 Qs
WB JEE 2010
2 Qs
WB JEE 2009
3 Qs
WB JEE 2008
7 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520252View paper
WB JEE 202520253View paper
WB JEE 202420242View paper
WB JEE 202320233View paper
WB JEE 202220223View paper
WB JEE 202120213View paper
WB JEE 202020202View paper
WB JEE 201920195View paper
WB JEE 201820184View paper
WB JEE 201720173View paper
WB JEE 201620163View paper
WB JEE 201120113View paper
WB JEE 201020102View paper
WB JEE 200920093View paper
WB JEE 200820087View paper

All Complex Numbers previous year questions

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

1
2016 · Mathematics · Algebra · Complex Numbers
WB JEE 2016
If \(\omega\) is an imaginary cube root of unity, then the value of (2 \(-\) \(\omega\)) (2 \(-\) \(\omega\)2) + 2(3 \(-\) \(\omega\))(3 \(-\) \(\omega\)2) + ... + (n \(-\) 1) (n \(-\) \(\omega\))(n \(-\) \(\omega\)2) is
A
\({{{n^2}} \over 4}{(n + 1)^2} - n\)
B
\({{{n^2}} \over 4}{(n + 1)^2} + n\)
C
\({{{n^2}} \over 4}{(n + 1)^2}\)
D
\({{{n^2}} \over 4}(n + 1) - n\)
Open complete paper
2
2016 · Mathematics · Algebra · Complex Numbers
WB JEE 2016
If z = sin\(\theta\) \(-\) icos\(\theta\), then for any integer n,
A
\({z^n} + {1 \over {{z^n}}} = 2\cos \left( {{{n\pi } \over 2} - n\theta } \right)\)
B
\({z^n} + {1 \over {{z^n}}} = 2\sin \left( {{{n\pi } \over 2} - n\theta } \right)\)
C
\({z^n} - {1 \over {{z^n}}} = 2i\sin \left( {n\theta - {{n\pi } \over 2}} \right)\)
D
\({z^n} - {1 \over {{z^n}}} = 2i\cos \left( {{{n\pi } \over 2} - n\theta } \right)\)
Open complete paper
3
2016 · Mathematics · Algebra · Complex Numbers
WB JEE 2016
The value of \(\sum\limits_{n = 1}^{13} {({i^n} + {i^{n + 1}})}\), \(i = \sqrt { - 1}\) is
A
i
B
i \(-\) 1
C
1
D
0
Open complete paper
4
2017 · Mathematics · Algebra · Complex Numbers
WB JEE 2017
Let z = x + iy, where x and y are real. The points (x, y) in the X-Y plane for which \({{{z + i} \over {z - i}}}\) is purely imaginary, lie on
A
a straight line
B
an ellipse
C
a hyperbola
D
a circle
Open complete paper
5
2017 · Mathematics · Algebra · Complex Numbers
WB JEE 2017
The complex number z satisfying the equation | z \(-\) 1 | = | z + 1 | = 1 is
A
0
B
1 + i
C
\(-\) 1 + i
D
1 \(-\) i
Open complete paper
6
2017 · Mathematics · Algebra · Complex Numbers
WB JEE 2017
The expression \({{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}\) equals
A
\(- {i^{n + 1}}\)
B
\({i^{n + 1}}\)
C
\(- {2i^{n + 1}}\)
D
1
Open complete paper
7
2018 · Mathematics · Algebra · Complex Numbers
WB JEE 2018
If z1 and z2 be two non-zero complex numbers such that \({{{z_1}} \over {{z_2}}} + {{{z_2}} \over {{z_1}}} = 1\), then the origin and the points represented by z1 and z2
A
lie on a straight line
B
form a right angled triangle
C
form an equilateral triangle
D
form an isosceles triangle
Open complete paper
8
2018 · Mathematics · Algebra · Complex Numbers
WB JEE 2018
If \({Z_r} = \sin {{2\pi r} \over {11}} - i\cos {{2\pi r} \over {11}}\), then \(\sum\limits_{r = 0}^{10} {{Z_r}}\) is equal to
A
\(-\) 1
B
0
C
i
D
\(-\) i
Open complete paper
9
2018 · Mathematics · Algebra · Complex Numbers
WB JEE 2018
Let z1 and z2 be complex numbers such that z1 \(\ne\) z2 and |z1| = |z2|. If Re(z1) > 0 and Im(z2) < 0, then \({{{z_1} + {z_2}} \over {{z_1} - {z_2}}}\) is
A
one
B
real and positive
C
real and negative
D
purely imaginary
Open complete paper
10
2018 · Mathematics · Algebra · Complex Numbers
WB JEE 2018
If \({a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}\),

then the value of \(\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{a_4}} & {{a_5}} & {{a_6}} \cr {{a_7}} & {{a_8}} & {{a_9}} \cr } } \right|\) is equal to
A
1
B
\(-\) 1
C
0
D
2
Open complete paper
11
2019 · Mathematics · Algebra · Complex Numbers
WB JEE 2019
Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z \(-\) arg(\(-\) z) is
A
\({\pi \over 2}\)
B
\(\pm\) \(\pi\)
C
\(\pi\)
D
\(-\) \(\pi\)
Open complete paper
12
2019 · Mathematics · Algebra · Complex Numbers
WB JEE 2019
For any non-zero complex number z, the minimum value of | z | + | z \(-\) 1 | is
A
1
B
\({{1 \over 2}}\)
C
0
D
\({{3 \over 2}}\)
Open complete paper
13
2019 · Mathematics · Algebra · Complex Numbers
WB JEE 2019
The polar coordinate of a point P is \(\left( {2, - {\pi \over 4}} \right)\). The polar coordinate of the point Q which is such that line joining PQ is bisected perpendicularly by the initial line, is
A
\(\left( {2,{\pi \over 4}} \right)\)
B
\(\left( {2,{\pi \over 6}} \right)\)
C
\(\left( { - 2,{\pi \over 4}} \right)\)
D
\(\left( { - 2,{\pi \over 6}} \right)\)
Open complete paper
14
2019 · Mathematics · Algebra · Complex Numbers
WB JEE 2019
The general value of the real angle \(\theta\), which satisfies the equation, \((\cos \theta + i\sin \theta )(\cos 2\theta + i\sin 2\theta )...(\cos n\theta + i\sin n\theta ) = 1\) is given by, (assuming k is an integer)
A
\({{2k\pi } \over {n + 2}}\)
B
\({{4k\pi } \over {n(n + 1)}}\)
C
\({{4k\pi } \over {n + 1}}\)
D
\({{6k\pi } \over {n(n + 1)}}\)
Open complete paper
15
2019 · Mathematics · Algebra · Complex Numbers
WB JEE 2019
If \(\theta \in R\) and \({{1 - i\cos \theta } \over {1 + 2i\cos \theta }}\) is real number, then \(\theta\) will be (when I : Set of integers)
A
\((2n + 1){\pi \over 2},n \in I\)
B
\({{3n\pi } \over 2},n \in I\)
C
\(n\pi ,n \in I\)
D
\(2n\pi ,n \in I\)
Open complete paper
16
2020 · Mathematics · Algebra · Complex Numbers
WB JEE 2020
The equation \(z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0\) represents a circle of radius
A
2 unit
B
3 unit
C
4 unit
D
6 unit
Open complete paper
17
2020 · Mathematics · Algebra · Complex Numbers
WB JEE 2020
The number of complex numbers p such that \(\left| p \right| = 1\) and imaginary part of p4 is 0, is
A
4
B
2
C
8
D
infinitely many
Open complete paper
18
2021 · Mathematics · Algebra · Complex Numbers
WB JEE 2021
Let C denote the set of all complex numbers. Define A = {(z, w) | z, w\(\in\)C and |z| = |w|}, B = {z, w} | z, w\(\in\)C and z2 = w2}. Then
A
A = B
B
A \(\subset\) B
C
B \(\subset\) A
D
A \(\cap\) B = \(\varphi\)
Open complete paper
19
2021 · Mathematics · Algebra · Complex Numbers
WB JEE 2021
If \(\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0\) for a complex number z, then z is equal to
A
\(\sqrt 2 (1 + i)\)
B
\(\sqrt 2 (1 - i)\)
C
\(\sqrt 2 ( - 1 + i)\)
D
\(\sqrt 2 ( - 1 - i)\)
Open complete paper
20
2021 · Mathematics · Algebra · Complex Numbers
WB JEE 2021
If |z| = 1 and z \(\ne\) \(\pm\) 1, then all the points representing \({z \over {1 - {z^2}}}\) lie on
A
a line not passing through the origin
B
the line y = x
C
the X-axis
D
the Y-axis
Open complete paper

Showing 20 of 48 questions