AP EAPCET 2024 - 20th May Morning Shift | Complex Numbers Question 21 | Mathematics

If the point $P$ represents the complex number $z=x+i y$ in the argand plane and if $\frac{z+i}{z-i}$ is a purely imaginary number, then the locus of $P$ is

$x^2+y^2+x-y=0$ and $(x, y) \neq(1,0)$

$x^2+y^2-x+y=0$ and $(x, y) \neq(1,0)$

$x^2+y^2-x+y=0$ and $(x, y)=(1,0)$

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

AP EAPCET 2024 - 20th May Morning Shift

MCQ (Single Correct Answer)

-0

$S=\{z \in C /|z+1-i|=1\}$ represents

the circle with centre at $(-1,1)$ and radius 1 unit

the circle with cente at $(1,-1)$ and radius 1 unit

the closed circular disc with centre at $(1,-1)$ and radius 1 unt

the closed circular disc with centre at( $-1,1$ ) and radius 1 unt

AP EAPCET 2024 - 19th May Evening Shift

MCQ (Single Correct Answer)

-0

If $m, n$ are respectively the least positive and greatest negative integer value of $k$ such that $\left(\frac{1-i}{1+i}\right)^k=-i$, then $m-n=$

AP EAPCET 2024 - 19th May Evening Shift

MCQ (Single Correct Answer)

-0

If a complex number $z$ is such that $\frac{z-2 i}{z-2}$ is purely imaginary number and the locus of $z$ is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is $\frac{z-2 i}{z-2}$

$2 \pi$

$\frac{\pi}{2}$

$\pi$

$\frac{\pi}{4}$

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