Question 1118071
| z - 2 - 3i | < 4   ==>  { All the points where the distance from z to 2+3i  is less than 4 }
3 < | z - 2 - 3i |   ==>  { All the points where the distance from z to 2+3i is greater than 3 }

Therefore,  3 < |z - 2 - 3i | < 4  is the intersection of those two sets. <br> 

That intersection is a ring centered on  2+3i  where the inner radius of the ring is 3 and the outer radius is 4 (only the space interior to these two radii are part of the solution, as  both sides have strict inequalities - see the area between the blue and green circles below).  <br>

{{{ drawing(400,400, -10, 10, -10, 10, grid(0),
                   blue(circle(2,3, 3)),
                   green(circle(2,3, 4)),
                   red(line(2,3,2,3))
  )
}}}

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Edited to change “union” to “intersection”