Originally Posted by

**mr fantastic** Geometrically, |z - 3| = 5 gives all the points a distance of 5 from z = 3. This is a circle with radius 5 and centre at z = 3, that is, (3, 0). So the Cartesian equation is $\displaystyle (x - 3)^2 + y^2 = 5^2$. You want the inside of this circle and its boundary.

Similarly, |z + i| = 1 <=> |z - (-i)| = 1 gives all the points a distance of 1 from z = -i. This is a circle with radius 5 and centre at z = -i, that is, (0, -1). So the Cartesian equation is $\displaystyle x^2 + (y + 1)^2 = 1^2$. You want the outside of this circle and its boundary.

To do it algebraically, I'll return later ....