JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Complex Numbers

More JEE Advanced questions on Complex Numbers

1. Let
   

   $$\alpha =\left(1-2\cos \left(\frac{\pi }{11}\right)\right)\left(1-2\cos \left(\frac{3\pi }{11}\right)\right)\left(1-2\cos \left(\frac{9\pi }{11}\right)\right)\left(1-2\cos \left(\frac{27\pi }{11}\right)\right)\left(1-2\cos \left(\frac{81\pi }{11}\right)\right).$$

   
   Then …
   JEE Advanced 2026 Copy linkView solution →
2. 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
   

   $$S=\left\{(x,y)\in \mathbb{R}\times \mathbb{R}:\left|x+iy-z_1\right|=2\left|x+iy-z_2\right|\right\}.$$

   
   Then which of the fo …
   JEE Advanced 2025 Copy linkView solution →
3. 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
   

   $$\alpha =\arg \left(\sum _{n=1}^{2025}(-\omega {)}^n\right).$$

   
   Then the …
   JEE Advanced 2025 Copy linkView solution →
4. 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 …
   JEE Advanced 2024 Copy linkView solution →
5. 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 …
   JEE Advanced 2023 Copy linkView solution →
6. Let $\mathrm{A}=\left\{\frac{1967+1686\mathrm{i}\sin \theta }{7-3\mathrm{i}\cos \theta }:\theta \in \mathbb{R}\right\}$. If A contains exactly one positive integer n, then the value of n is
   JEE Advanced 2023 Copy linkView solution →