Question

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

• A. $(2,0)$
• B. $(0,2)$
• C. $(0,0)$
• D. $(0,-2)$

Answer 1

Answer: (D)

$(0,-2)$

Answer 2

The correct answer is (D) : $(0,-2)$
(z−2i)(z+2i)=4(z+i)(z−i)
zz+4+2i(z−z)=4(zz+1+i(z−z))
3zz−6i(z−z)=0
x2+y2−2i(2iy)=0
x2+y2+4y=0