Complex Numbers PYQs - Last 5 Years
JEE Advanced / Mathematics / Algebra / 12 recent questions
MathematicsAlgebra2022-2026
Practice 12 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.
12
PYQs on Page
Mathematics / Algebra
2022-2026
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12
Last 5 Years
2022-2026
12
Last 10 Years
2017-2026
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12PYQs
INTEGER50%
MCQM33.3%
MCQ16.7%
Difficulty Mix
#1 Hard6
#2 Medium6
12 in last 5 years12 in last 10 years
Last 5 Years Complex Numbers Questions
Showing 12 of 12 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