SOLUTION: What is the region represented by the inequality 3 < |z - 2 - 3i| < 4 in the argand plane.
According to my solution
I assume the value of Z = x+ yi and the final equation I have
Question 1118071: What is the region represented by the inequality 3 < |z - 2 - 3i| < 4 in the argand plane.
According to my solution
I assume the value of Z = x+ yi and the final equation I have got on solving, is like that
9 < x^2 + y^2 - 4x - 6y + 13 < 16.
Now I am unable to solve further. Please explain it Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! | 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.
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).
——————-
Edited to change “union” to “intersection”
