Question 1209633
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Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.
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        In his post, @CPhill came to the conclusion that  z = -4 
        is the solution  (one solution)  to the problem.


        But easy check shows that it is not so.



<pre>
Indeed, then |z-1| = |-4-1| = |-5| = 5;

             |z+3| = |-4+3| = |-1| = 1,

             |z-2i| = |-4-2i| = {{{sqrt((-4)^2+(-2)^2)}}} = {{{sqrt(20)}}} = {{{2*sqrt(5)}}},

but  5 is not equal to  {{{1 + 2*sqrt(5)}}}.
</pre>

So, it disproves the statement by @CPhill that z= 4 is a solution.


It is not.