# Plot complex region

1. Apr 17, 2010

### Mechdude

1. The problem statement, all variables and given/known data
i was supposed to figure out what this region looks like ad to plot it
$$\left| \frac{z + i}{z - i} \right| > 1$$

2. Relevant equations

$z = x + iy$

3. The attempt at a solution

i tried a couple of rearrangements but i got nowhere:
$$\left|z+i \right| > \left| z - i \right|$$
getting:
$$\sqrt{ x^2 + (y+1)^2 } > \sqrt{ x^2 + (y-1)^2 }$$

which ends up $$4y > 0$$
is this it? simply y>0?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 17, 2010

### annoymage

i think, im not sure, but try something like this

|a| > |b|

=> a > |b| or a < -|b|

=> -a < b < a or a < b < -a

=> (b > -a and b < a ) or (b > a and b < -a)

and plot

Last edited: Apr 17, 2010