1
JEE Advanced 2024 Paper 1 Online
Numerical
+4
-0

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 all the roots of the equation $f(x)=0$, then $\left|\alpha_1\right|^2+\left|\alpha_2\right|^2+\left|\alpha_3\right|^2+\left|\alpha_4\right|^2$ is equal to ____________.

2
JEE Advanced 2023 Paper 1 Online
Numerical
+4
-0
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
3
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0
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 _________.
4
JEE Advanced 2022 Paper 1 Online
Numerical
+3
-0
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 _________.
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12