Complex Numbers PYQs - Last 10 Years
JEE Advanced / Mathematics / Algebra / 21 recent questions
MathematicsAlgebra2017-2026
Practice 21 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.
21
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Mathematics / Algebra
2017-2026
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2022-2026
21
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2017-2026
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21PYQs
MCQM42.9%
INTEGER38.1%
MCQ19%
Difficulty Mix
#1 Medium13
#2 Hard8
12 in last 5 years21 in last 10 years
Last 10 Years Complex Numbers Questions
Showing 21 of 21 filtered questions.
1Complex Numbers
Let $\mathbb{R}$ denote the set of all real numbers and let $i=\sqrt{-1}$. Consider the matrices
$$ S=\left[\begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array}\right] \quad \text { and } \quad T=\left[\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\...
$$ S=\left[\begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array}\right] \quad \text { and } \quad T=\left[\begin{array}{ll} 1 & 1 \\ 0 & 1 \end{array}\...
MCQM+4 / -12026
2Complex Numbers
Match each entry in List-I to the correct entry in List-II and choose the correct option.
table {
width: 100%;
border-collapse: collapse;
margin: 20px 0;
}
th {
background-color: blue;
color: w...
table {
width: 100%;
border-collapse: collapse;
margin: 20px 0;
}
th {
background-color: blue;
color: w...
MCQ+4 / -12026
3Complex Numbers
Let$$ \alpha = \left( 1 - 2\cos\left(\frac{\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{3\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{9\pi}{11}\right) \right) \left( 1 - 2\cos\left(\frac{27\pi}{11}\right) \right) \left( 1 - 2\...
INTEGER+4 / -02026
4Complex Numbers
For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi<\arg (z) \leq \pi$. Let $\omega$ be the cube root of unity for which $0<\arg (\omega)<\pi$. Let
$$ \alpha=\arg \left(\sum\limits_{n=1}^{2025}...
$$ \alpha=\arg \left(\sum\limits_{n=1}^{2025}...
INTEGER+4 / -02025
5Complex Numbers
Let ℝ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers, where $i = \sqrt{-1}$. Let\(S = \{(x, y) \in \mathbb{R} \times \mathbb{R} : |x + iy - z_1| = 2|x + iy - z_2| \}.\)Then which of the followin...
MCQM+4 / -22025
6Complex Numbers
Let $f(x)=x^4+a x^3+b x^2+c$ be a polynomial with real coefficients such that $f(1)=-9$. Suppose that $i \sqrt{3}$ is a root of the equation $4 x^3+3 a x^2+2 b x=0$, where $i=\sqrt{-1}$. If $\alpha_1, \alpha_2, \alpha_3$, and $\alpha_4$ are...
INTEGER+4 / -02024
7Complex Numbers
Let $S=\{a+b \sqrt{2}: a, b \in \mathbb{Z}\}, T_1=\left\{(-1+\sqrt{2})^n: n \in \mathbb{N}\right\}$, and $T_2=\left\{(1+\sqrt{2})^n: n \in \mathbb{N}\right\}$. Then which of the following statements is (are) TRUE?
MCQM+4 / -22024
8Complex Numbers
Let $z$ be a complex number satisfying $|z|^3+2 z^2+4 \bar{z}-8=0$, where $\bar{z}$ denotes the complex conjugate of $z$. Let the imaginary part of $z$ be nonzero.
Match each entry in List-I to the correct entries in List-II.
.tg {border-...
Match each entry in List-I to the correct entries in List-II.
.tg {border-...
MCQ+3 / -12023
9Complex Numbers
Let $A=\left\{\frac{1967+1686 i \sin \theta}{7-3 i \cos \theta}: \theta \in \mathbb{R}\right\}$. If $A$ contains exactly one positive integer $n$, then the value of $n$ is
INTEGER+4 / -02023
10Complex Numbers
Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of
\((\bar{z})^{2}+\frac{1}{z^{2}}\)
are integers, then which of the following is/are possib...
\((\bar{z})^{2}+\frac{1}{z^{2}}\)
are integers, then which of the following is/are possib...
MCQM+4 / -22022
11Complex Numbers
Let \(\bar{z}\) denote the complex conjugate of a complex number \(z\) and let \(i=\sqrt{-1}\). In the set of complex numbers, the number of distinct roots of the equation
\(\bar{z}-z^{2}=i\left(\bar{z}+z^{2}\right)\)
is _________.
\(\bar{z}-z^{2}=i\left(\bar{z}+z^{2}\right)\)
is _________.
INTEGER+3 / -02022
12Complex Numbers
Let \(z\) be a complex number with a non-zero imaginary part. If
\(\frac{2+3 z+4 z^{2}}{2-3 z+4 z^{2}}\)
is a real number, then the value of \(|z|^{2}\) is _________.
\(\frac{2+3 z+4 z^{2}}{2-3 z+4 z^{2}}\)
is a real number, then the value of \(|z|^{2}\) is _________.
INTEGER+3 / -02022
13Complex Numbers
For any complex number w = c + id, let \(\arg (w) \in ( - \pi ,\pi ]\), where \(i = \sqrt { - 1}\). Let \(\alpha\) and \(\beta\) be real numbers such that for all complex numbers z = x + iy satisfying $$\arg \left( {{{z + \alpha } \over {z...
MCQM+4 / -22021
14Complex Numbers
Let $\theta_1, \theta_2, \ldots, \theta_{10}$ be positive valued angles (in radian) such that $\theta_1+\theta_2+\cdots+\theta_{10}=2 \pi$. Define the complex numbers $z_1=e^{i \theta_1}, z_k=z_{k-1} e^{i \theta_k}$ for $k=2,3, \ldots, 10$,...
MCQ+3 / -12021
15Complex Numbers
For a complex number z, let Re(z) denote that real part of z. Let S be the set of all complex numbers z satisfying \({z^4} - |z{|^4} = 4i{z^2}\), where i = \(\sqrt { - 1}\). Then the minimum possible value of |z1 \(-\) z2|2, where z1, z2$$...
INTEGER+3 / -12020
16Complex Numbers
Let S be the set of all complex numbers z satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?
MCQM+4 / -22020
17Complex Numbers
Let \(\omega \ne 1\) be a cube root of unity. Then the minimum of the set \(\{ {\left| {a + b\omega + c{\omega ^2}} \right|^2}:a,b,c\) distinct non-zero integers} equals ..................
INTEGER+3 / -02019
18Complex Numbers
Let S be the set of all complex numbers z satisfying \(\left| {z - 2 + i} \right| \ge \sqrt 5\). If the complex number z0 is such that \({1 \over {\left| {{z_0} - 1} \right|}}\) is the maximum of the set $$\left\{ {{1 \over {\left| {{z_0} ...
MCQ+3 / -12019
19Complex Numbers
Let s, t, r be non-zero complex numbers and L be the set of solutions \(z = x + iy(x,y \in R,\,i = \sqrt { - 1} )\) of the equation \(sz + t\overline z + r = 0\) where \(\overline z\) = x \(-\) iy. Then, which of the following statement(s...
MCQM+4 / -12018
20Complex Numbers
For a non-zero complex number z, let arg(z) denote the principal argument with \(-\) \(\pi\) < arg(z) \(\le\) \(\pi\). Then, which of the following statement(s) is (are) FALSE?
MCQM+4 / -12018
21Complex Numbers
Let a, b, x and y be real numbers such that a \(-\) b = 1 and y \(\ne\) 0. If the complex number z = x + iy satisfies \({\mathop{\rm Im}\nolimits} \left( {{{az + b} \over {z + 1}}} \right) = y\), then which of the following is(are) possi...
MCQM+4 / -12017