Complex Numbers PYQs - Last 10 Years
JEE Main / Mathematics / Algebra / 180 recent questions
MathematicsAlgebra2017-2026
Practice 180 JEE Main Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
180
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Mathematics / Algebra
2017-2026
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112
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2022-2026
180
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2017-2026
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180PYQs
MCQ78.3%
INTEGER21.7%
Difficulty Mix
#1 Medium156
#2 Hard16
#3 Easy8
112 in last 5 years180 in last 10 years
Last 10 Years Complex Numbers Questions
Showing 30 of 180 filtered questions.
1Complex Numbers
Let \(u = {{2z + i} \over {z - ki}}\), z = x + iy and k > 0. If the curve represented by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :
MCQ+4 / -12020
2Complex Numbers
If a and b are real numbers such that \({\left( {2 + \alpha } \right)^4} = a + b\alpha\) where \(\alpha = {{ - 1 + i\sqrt 3 } \over 2}\) then a + b is
equal to :
equal to :
MCQ+4 / -12020
3Complex Numbers
If \({\left( {{{1 + i} \over {1 - i}}} \right)^{{m \over 2}}} = {\left( {{{1 + i} \over {1 - i}}} \right)^{{n \over 3}}} = 1\), (m, n
\(\in\) N) then the
greatest common divisor of the least values of
m and n is _______ .
\(\in\) N) then the
greatest common divisor of the least values of
m and n is _______ .
INTEGER+4 / -02020
4Complex Numbers
If z1
, z2
are complex numbers such that
Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and
arg(z1 - z2) = \({\pi \over 6}\), then Im(z1
+ z2
) is equal to :
, z2
are complex numbers such that
Re(z1) = |z1 – 1|, Re(z2) = |z2 – 1| , and
arg(z1 - z2) = \({\pi \over 6}\), then Im(z1
+ z2
) is equal to :
MCQ+4 / -12020
5Complex Numbers
The value of \({\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}\) is :
MCQ+4 / -12020
6Complex Numbers
The imaginary part of
\({\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}\) can be :
\({\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}\) can be :
MCQ+4 / -12020
7Complex Numbers
Let
A = \(\left\{ {\theta \in \left( { - {\pi \over 2},\pi } \right):{{3 + 2i\sin \theta } \over {1 - 2i\sin \theta }}is\,purely\,imaginary} \right\}\)
. Then the sum of the elements in A is :
A = \(\left\{ {\theta \in \left( { - {\pi \over 2},\pi } \right):{{3 + 2i\sin \theta } \over {1 - 2i\sin \theta }}is\,purely\,imaginary} \right\}\)
. Then the sum of the elements in A is :
MCQ+4 / -12019
8Complex Numbers
Let \(\alpha\) and \(\beta\) be two roots of the equation x2 + 2x + 2 = 0 , then \(\alpha ^{15}\) + \(\beta ^{15}\) is equal to :
MCQ+4 / -12019
9Complex Numbers
Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz\(_0^{81}\) \(-\) 3iz\(_0^{93}\), then arg z is equal to :
MCQ+4 / -12019
10Complex Numbers
All the points in the set
\(S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )\) lie on a :
\(S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )\) lie on a :
MCQ+4 / -12019
11Complex Numbers
Let z \(\in\) C be such that |z| < 1.
If \(\omega = {{5 + 3z} \over {5(1 - z)}}\)z, then :
If \(\omega = {{5 + 3z} \over {5(1 - z)}}\)z, then :
MCQ+4 / -12019
12Complex Numbers
If \(\alpha\) and \(\beta\) be the roots of the equation
x2 – 2x + 2 = 0, then the least value of n for which \({\left( {{\alpha \over \beta }} \right)^n} = 1\) is :
x2 – 2x + 2 = 0, then the least value of n for which \({\left( {{\alpha \over \beta }} \right)^n} = 1\) is :
MCQ+4 / -12019
13Complex Numbers
If \(z = {{\sqrt 3 } \over 2} + {i \over 2}\left( {i = \sqrt { - 1} } \right)\),
then (1 + iz + z5 + iz8)9 is equal to :
then (1 + iz + z5 + iz8)9 is equal to :
MCQ+4 / -12019
14Complex Numbers
If \({{z - \alpha } \over {z + \alpha }}\left( {\alpha \in R} \right)\) is a purely imaginary number and | z | = 2, then a value of \(\alpha\) is :
MCQ+4 / -12019
15Complex Numbers
Let z1 and z2 be two complex numbers satisfying | z1 | = 9 and | z2 – 3 – 4i | = 4. Then the minimum value of
| z1 – z2 | is :
| z1 – z2 | is :
MCQ+4 / -12019
16Complex Numbers
The equation |z – i| = |z – 1|, i = \(\sqrt { - 1}\), represents :
MCQ+4 / -12019
17Complex Numbers
Let z \(\in\) C with Im(z) = 10 and it satisfies \({{2z - n} \over {2z + n}}\) = 2i - 1 for some natural number n. Then :
MCQ+4 / -12019
18Complex Numbers
Let \({\left( { - 2 - {1 \over 3}i} \right)^3} = {{x + iy} \over {27}}\left( {i = \sqrt { - 1} } \right),\,\,\) where x and y are real numbers, then y \(-\) x equals :
MCQ+4 / -12019
19Complex Numbers
Let z be a complex number such that |z| + z = 3 + i (where i = \(\sqrt { - 1}\)). Then |z| is equal to :
MCQ+4 / -12019
20Complex Numbers
Let z1 and z2 be any two non-zero complex numbers such that \(3\left| {{z_1}} \right| = 4\left| {{z_2}} \right|.\) If \(z = {{3{z_1}} \over {2{z_2}}} + {{2{z_2}} \over {3{z_1}}}\) then :
MCQ+4 / -12019
21Complex Numbers
Let \(z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5}.\) If R(z) and 1(z) respectively denote the real and imaginary parts of z, then :
MCQ+4 / -12019
22Complex Numbers
If a > 0 and z = \({{{{\left( {1 + i} \right)}^2}} \over {a - i}}\), has magnitude \(\sqrt {{2 \over 5}}\), then \(\overline z\) is equal to :
MCQ+4 / -12019
23Complex Numbers
If z and w are two complex numbers such that |zw| = 1 and arg(z) – arg(w) = \({\pi \over 2}\)
, then :
, then :
MCQ+4 / -12019
24Complex Numbers
The least positive integer n for which \({\left( {{{1 + i\sqrt 3 } \over {1 - i\sqrt 3 }}} \right)^n} = 1,\) is :
MCQ+4 / -12018
25Complex Numbers
The set of all \(\alpha\) \(\in\) R, for which w = \({{1 + \left( {1 - 8\alpha } \right)z} \over {1 - z}}\) is purely imaginary number, for all z \(\in\) C satisfying |z| = 1 and Re z \(\ne\) 1, is :
MCQ+4 / -12018
26Complex Numbers
If |z \(-\) 3 + 2i| \(\le\) 4 then the difference between the greatest value and the least value of |z| is :
MCQ+4 / -12018
27Complex Numbers
If \(\alpha ,\beta \in C\) are the distinct roots of the equation
x2 - x + 1 = 0, then \({\alpha ^{101}} + {\beta ^{107}}\) is equal to :
x2 - x + 1 = 0, then \({\alpha ^{101}} + {\beta ^{107}}\) is equal to :
MCQ+4 / -12018
28Complex Numbers
The equation
Im \(\left( {{{iz - 2} \over {z - i}}} \right)\) + 1 = 0, z \(\in\) C, z \(\ne\) i
represents a part of a circle having radius
equal to :
Im \(\left( {{{iz - 2} \over {z - i}}} \right)\) + 1 = 0, z \(\in\) C, z \(\ne\) i
represents a part of a circle having radius
equal to :
MCQ+4 / -12017
29Complex Numbers
Let z\(\in\)C, the set of complex numbers. Then the equation, 2|z + 3i| \(-\) |z \(-\) i| = 0 represents :
MCQ+4 / -12017
30Complex Numbers
Let \(\omega\) be a complex number such that 2\(\omega\) + 1 = z where z = \(\sqrt {-3}\). If
$$\left| {\matrix{
1 & 1 & 1 \cr
1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr
1 & {{\omega ^2}} & {{\omega ^7}} \cr
} } \right...
$$\left| {\matrix{
1 & 1 & 1 \cr
1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr
1 & {{\omega ^2}} & {{\omega ^7}} \cr
} } \right...
MCQ+4 / -12017