1. Apr 2, 2009

### atwong713

when indicating the region of the complex plane that corresponds to all points z that satisfy the condition
|z|=11
this region would be the circle of radius 11 around the origin because the |z-w| is the distance between z and w, where z and w are both complex numbers
in general |z-w|=r would be a circle around the pt w on the complex plane with radius r

but how would you indicate a region that satisfies |2z+1| = 3 or |i-2z|=5 for all z?
what do these represent geometrically?

2. Apr 2, 2009

### HallsofIvy

Staff Emeritus
|2z+1|= |2(z+1/2)|= 2|z+ 1/2|= 3 so |z+ 1/2|= 3/2.