# Math Help - complex inequality

1. ## complex inequality

$\frac{|z-2|}{|z+3i|}<1$

I tried:

$z=x+iy$

$\frac{\sqrt{(x-2)^2+y^2}}{\sqrt{x^2+(y+3)^2}}<1$

then i got stuck. I need to solve it and i think i'll have a circle equation.

2. By the way, this is urgent. I'd be glad if you can take a look at it.

3. Squaring I get $0<2x+6y+5$ which an upper half-plane.
You can see that $z=0,~z=1,~z=i~\&~z=1+i$ all work.

4. i think it should be 4x not 2x. But i got it, thanks.