If z=x+i y satisfies |z|-2=0 and |z-i|-|z+5 i|=0, then :

Question

If $z=x+i y$ satisfies $|z|-2=0$ and $|z-i|-|z+5 i|=0$, then :

Accepted Answer

$|z - i| = |z + 5i|$

So, $$\mathrm{z}$$ lies on $${ \bot ^r}$$ bisector of $(0,1)$ and $(0, - 5)$

i.e., line $y =  - 2$

as $|z| = 2$

$$ \Rightarrow z =  - 2i$$

$x = 0$ and $y =  - 2$

so, $x + 2y + 4 = 0$

Solutions · 1