TS EAMCET 2023 (Online) 14th May Evening Shift | Complex Numbers Question 50 | Mathematics

List - I		List - II
(i)	$$ \frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma} $$	(a)	-1
(ii)	$$ \alpha^3+\beta^3+\gamma^3 $$	(b)	-4
(iii)	$$ \alpha^4+\beta^4+\gamma^4 $$	(c)	1
(iv)	$$ (\alpha-\beta)^2+(\beta-\gamma)^2+(\gamma-\alpha)^2 $$	(d)	3
		(e)	0

Then, the correct match is

(i) $\rightarrow \mathrm{a}$, (ii) $\rightarrow \mathrm{a}$, (iii) $\rightarrow \mathrm{d}$, (iv) $\rightarrow \mathrm{b}$

(i) $\rightarrow \mathrm{c}$, (ii) $\rightarrow \mathrm{a}$, (iii) $\rightarrow \mathrm{e}$, (iv) $\rightarrow \mathrm{b}$

(i) $\rightarrow \mathrm{a}$, (ii) $\rightarrow \mathrm{c}$, (iii) $\rightarrow \mathrm{d}$, (iv) $\rightarrow \mathrm{b}$

(i) → c, (ii) → a, (iii) → b, (iv) → e

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $i=\sqrt{-1}$, then $\operatorname{Arg}\left[\frac{(1+i)^{2025}}{(1-i)^{2022}}\right]=$

$\frac{-\pi}{4}$

$\frac{\pi}{4}$

$\frac{3 \pi}{4}$

$\frac{-3 \pi}{4}$

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

The locus of $z$ such that $\left|\frac{z-i}{z+i}\right|=2$, where $z=x+i y$, is

$3 x^2+3 y^2+10 y+3=0$

$3 x^2-3 y^2-10 y-3=0$

$3 x^2+3 y^2+10 y-3=0$

$x^2+y^2-5 y+3=0$

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $x_n=\cos \frac{\pi}{2^n}+i \sin \frac{\pi}{2^n}$, then $\prod_{n=1}^{\infty} x_n=$

-1

$i$

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