Let z be a complex number such that |(z-2i)/(z+i) |=2 , zneq-i . Then z lies on the circle of radius 2 and centre :

Complex Numbers: Let z be a complex number such that |(z-2i)/(z+i) |=2 , zneq-i .… | JEE Main 2023

JEE Main 2023 (Online) 25th January Evening ShiftQuestion 1

Let $z$ be a complex number such that $\left|\frac{z-2i}{z+i}\right|=2$, $z\neq-i$. Then $z$ lies on the circle of radius $2$ and centre :

Complex Numbers

$(2,0)$$(0,2)$$(0,0)$$(0,-2)$✓ Correct answer

Solution

$|z-2i|^2=4|z+i|^2$: $x^2+(y-2)^2=4x^2+4(y+1)^2$, i.e. $x^2+y^2+4y=0$, centre $(0,-2)$, radius $2$.