1
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $i^2=-1$, then $(1+\sqrt{3} i)^{2022}-(\sqrt{3}-i)^{2022}=$

A

$2^{2023}$

B

0

C

$2^{2022}$

D

$3^{1011}$

2
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^4+\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^4=r$ cis $\theta$, then one of the values of $\sqrt{r \operatorname{cis} \theta}$ is

A

$\operatorname{cis}\left(\frac{3 \pi}{4}\right)$

B

$\operatorname{cis}\left(\frac{3 \pi}{2}\right)$

C

$\operatorname{cis}\left(\frac{\pi}{3}\right)$

D

$\operatorname{cis} \pi$

3
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $z=x+i y$ and the point $P$ in the argand plane represents $z$, then the locus of $z$ satisfying the equation $|z-2|+|z-2 i|=4$ is

A

$4 x^2+3 x y+4 y^2-6 x-6 y+8=0$

B

$3 x^2+2 x y+3 y^2-8 x-8 y+6=0$

C

$3 x^2+2 x y+3 y^2-8 x-8 y=0$

D

$4 x^2+3 x y+4 y^2-6 x-6 y=0$

4
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

One of the values of $(\sqrt{3}-i)^{2 / 5}$ is

A

$2^{\frac{2}{5}}(1-\sqrt{3} i)$

B

$2^{\frac{-3}{5}}(\sqrt{3}+i)$

C

$2^{\frac{2}{5}}(\sqrt{3}-i)$

D

$2^{\frac{-3}{5}}(1+\sqrt{3} i)$

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