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

Let $z=x+i y$ be a point in the argand plane. If the amplitude of $\left(\frac{z-3}{z+2 i}\right)$ is $\frac{\pi}{2}$, then the locus of $z$ is

A

a circle

B

a straight line

C

a semicircular arc not containing the origin

D

a semicircular arc containing the origin

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

If a point $P$ denotes the complex number $z=x+i y$ in the argand plane and if $\frac{z-(2+i)}{z+(1-2 i)}$ is purely real, then the locus of $P$ is

A

the line $x+3 y-5=0$ excluding the point $(-1,2)$

B

the circle $x^2+y^2-x-3 y=0$ excluding the point $(-1,2)$

C

the line $x+3 y-5=0$ and the circle $x^2+y^2-x-3 y=0$ excluding the point $(-1,2)$

D

the circle $x^2+y^2-2 x-6 y+5=0$ excluding the point $(-1,2)$

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

If $i$ is the root of the equation $x^2+1=0$, then

$$ (1+\sqrt{3} i)^{2023}+(1-\sqrt{3} i)^{2023}= $$

A

$2^{2022}$

B

$2^{2023}$

C

$2^{2022}(\sqrt{3})$

D

$2^{2023}(\sqrt{3})$

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

One of the values of $(\sqrt{3}-i)^{\frac{1}{6}}$ is

A

$2^{\frac{1}{6}}$ cis $\frac{61 \pi}{36}$

B

$2^{\frac{1}{6}}$ cis $\frac{37 \pi}{36}$

C

$2^{\frac{1}{6}}$ cis $\frac{59 \pi}{36}$

D

$2^{\frac{1}{6}}$ cis $\frac{49 \pi}{36}$

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