1
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

One of the roots of the equation $(x+1)^4+81=0$ is

A

$3\left(\frac{1+i}{\sqrt{2}}\right)$

B

$-\left(\frac{3+\sqrt{2}+3 i}{\sqrt{2}}\right)$

C

$-\left(\frac{3+\sqrt{2}+i}{\sqrt{2}}\right)$

D

$-\left(\frac{3+3 i}{\sqrt{2}}\right)$

2
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The amplitude of the complex number $\frac{(\sqrt{3}+i)(1-\sqrt{3} i)}{(-1+i)(-1-i)}$ is

A

$\frac{\pi}{2}$

B

$\frac{\pi}{3}$

C

$-\frac{5 \pi}{12}$

D

$-\frac{\pi}{6}$

3
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If a complex number $z=x+i y$ represents a point $p(x, y)$ in the argand plane and $z$ satisfies the condition that the imaginary part of $\frac{z-3}{z+3 i}$ is zero, then the locus of the point $P$ is

A

$x^2+y^2-3 x+3 y=0,(x, y) \neq(0,-3)$

B

$2 x y-3 x+3 y+9=0,(x, y) \neq(0,-3)$

C

$x-y-3=0,(x, y) \neq(0,-3)$

D

$x+y+3=0,(x, y) \neq(0,-3)$

4
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ (\sqrt{3}+i)^{10}+(\sqrt{3}-i)^{10}= $$

A

$1024 \sqrt{3}$

B

1024

C

2048

D

$512 \sqrt{3}$

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