JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Complex Numbers

Let

Then …

Let $\mathbb{R}$ 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

Then which of the fo …

For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi <\arg (z)\le \pi$. Let $\omega$ be the cube root of unity for which $0<\arg (\omega )<\pi$. Let

Then the …

Let $\mathrm{S}=\{\mathrm{a}+\mathrm{b}\sqrt{2}:\mathrm{a},\mathrm{b}\in \mathbb{Z}\},{\mathrm{T}}_1=\left\{(-1+\sqrt{2}{)}^{\mathrm{n}}:\mathrm{n}\in \mathbb{N}\right\}$ and ${\mathrm{T}}_2=\left\{(1+\sqrt{2}{)}^{\mathrm{n}}:\mathrm{n}\in \mathbb{N}\right\}$. Then which …

Let ${\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{A}}_3,\dots ,{\mathrm{A}}_8$ be the vertices of a regular octagon that lie on a circle of radius 2. Let P be a point on the circle and let ${\mathrm{PA}}_{\mathrm{i}}$ denote the distance between the points P and …

Let z be complex number satisfying $|z{|}^3+2z^2+4\bar{z}-8=0$, 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.

List-I
(P) $|z{|}^2$ is equal to
(Q) $|z-\bar{z}{|}^2$ is …