What points satisfy $\frac{|z-i|}{|z+i|}<1$

Question

Here's what I got so far

$$|z-i|<|z+i|$$ $$z^2-i2z-1<z^2+i2z-1$$ $$0<i4z$$

Answer 1

Geometrically $|z-i|=|z+i|$ shows all points which have the same distanse from $i$ and $-i$, they lie on $x$ axis so $|z-i|<|z+i|$ is the upper half plane.

Answer 2

Hint: $z$ is closer to ... than to ...

Answer 3

Hint: set $z=a+bi$ in your last unequality and find the geometric properties $(a, b)$ should have.