TG EAPCET 2024 (Online) 11th May Morning Shift | Complex Numbers Question 3 | Mathematics

$\alpha, \beta$ are the roots of the equation $x^{2}+2 x+4=0$. If the point representing $\alpha$ in the argand diagram lies in the 2nd quadrant and $\alpha^{2024}-\beta^{2024}=i k,(i=\sqrt{-1})$, then $k=$

$-2^{2025} \sqrt{3}$

$2^{2025} \sqrt{3}$

$-2^{2024} \sqrt{3}$

$2^{2004} \sqrt{3}$

TG EAPCET 2024 (Online) 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $z=x+i y$ satisfies the equation $z^{2}+a z+a^{2}=0, a \in R$, then

$|z|=|a|$

$|z-a|=|a|$

$z=|a|$

$z=a$

TG EAPCET 2024 (Online) 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $z_{1}, z_{2}, z_{3}$ are three complex numbers with unit modulus such that $\left|z_{1}-z_{2}\right|^{2}+\left|z_{1}-z_{3}\right|^{2}=4$, then $z_{1} \bar{z}_{2}+\bar{z}_{1} z_{2}+z_{1} \bar{z}_{3}+\bar{z}_{1} z_{3}=$

$\left|z_{2}\right|^{2}+\left|z_{3}\right|^{2}$

$\left|z_{1}\right|^{2}-\left|z_{2}+z_{3}\right|^{2}$

TG EAPCET 2024 (Online) 10th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\omega$ is the complex cube root of unity and

$\left(\frac{a+b \omega+c \omega^{2}}{c+a \omega+b \omega^{2}}\right)^{k}+\left(\frac{a+b \omega+c \omega^{2}}{b+a \omega^{2}+c \omega}\right)^{l}=2$, then $2 k+l$ is always

divisible by 2

divisible by 6

divisible by 3

divisible by 5

PREVIOUS NEXT

TS EAMCET Subjects