Complex Numbers and Quadratic Equations

JEE Advanced · Mathematics · 46 past questions

13 of 46 · show all

1. Q3 2025 Paper 1

   Let $\mathbb{R}$ denote the set of all real numbers. Let $z_1 = 1+2i$ and $z_2 = 3i$ be two complex numbers…

   Try it →
2. Q12 2021 Paper 1

   For any complex number $w=c+id$, let $\arg(w)\in(-\pi,\pi]$, where $i=\sqrt{-1}$. Let $\alpha$ and $\beta$ be…

   Try it →
3. Q15 2020 Paper 1

   Let $S$ be the set of all complex numbers $z$ satisfying $|z^2+z+1|=1$. Then which of the following…

   Try it →
4. Q17 2019 Paper 1

   Let $S$ be the set of all complex numbers $z$ satisfying $|z-2+i| \ge \sqrt{5}$. If the complex number $z_0$…

   Try it →
5. Q20 2018 Paper 2

   Let $s,t,r$ be non-zero complex numbers and $L$ be the set of solutions $z=x+iy$ ($x,y\in\mathbb{R}$…

   Try it →
6. Q24 2016 Paper 2

   Let $a,b\in\mathbb{R}$ and $a^2+b^2\neq0$. Suppose…

   Try it →
7. Q27 2013 Paper 1

   Let complex numbers $\alpha$ and $\dfrac{1}{\bar{\alpha}}$ lie on circles $(x - x_0)^2 + (y - y_0)^2 = r^2$…

   Try it →
8. Q28 2013 Paper 2

   Let $w = \frac{\sqrt{3}+i}{2}$ and $P = \{w^n : n = 1, 2, 3, \ldots\}$. Further…

   Try it →
9. Q29 2013 Paper 2

   Paragraph for Questions 49 and 50…

   Try it →
10. Q30 2013 Paper 2

    Paragraph for Questions 49 and 50…

    Try it →
11. Q33 2011 Paper 1

    If $z$ is any complex number satisfying $|z - 3 - 2i| \le 2$, then the minimum value of $|2z - 6 + 5i|$ is

    Try it →
12. Q36 2010 Paper 1

    Let $z_1$ and $z_2$ be two distinct complex numbers and let $z = (1-t)z_1 + tz_2$ for some real number $t$…

    Try it →
13. Q46 2007 Paper 2

    If $|z| = 1$ and $z \neq \pm 1$, then all the values of $\dfrac{z}{1-z^2}$ lie on

    Try it →