Question

Find the points of the plane which satisfy the following equations:
$|z+2i|=|z+2|$

Answer 1

Let $z=x+iy$

Then, $|x+iy+2i|-|x+iy+2|=0$

$⟹\sqrt{x^2+(y+2{)}^2}=\sqrt{(x+2{)}^2+y^2}$

$⟹x^2+y^2+4y+4=x^2+4x+4+y^2$........[squaring both sides]

$⟹4x-4y=0⟹x=y$......[equation of a straight line]

Hence all the points which lie on the above line will satisfy the equations