- #1
zeromaxxx
- 17
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Homework Statement
Determine the region in the complex plane described by |z-2i| < |z+ i|
Homework Equations
z= x+ iy
|z|= (x2 + y2)1/2
The Attempt at a Solution
|z-2i| < |z+ i|
|z-2i|/|z+ i| < 1
|z-2i| = [(x-2i)2 + y2]1/2
|z+ i| = [(x+i)2 + y2]1/2
[(x-2i)2 + y2]1/2
--------------- < 1
[(x+i)2 + y2]1/2
[(x-2i)2 + y2]1/2*[(x+i)2 - y2]1/2
---------------------------------- < 1
[(x+i)2 + y2]1/2*[(x+i)2 - y2]1/2
Am I on the right track of solving this so far? If so how do I proceed to the next step? If not what part did I do wrong? Any feedback is appreciated!