document.write( "Question 1209633: Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|.
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Algebra.Com's Answer #849744 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "        In his post, @CPhill came to the conclusion that z = -4
\n" ); document.write( "        is the solution (one solution) to the problem.\r
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\n" ); document.write( "\n" ); document.write( "        But easy check shows that it is not so.\r
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document.write( "Indeed, then |z-1| = |-4-1| = |-5| = 5;\r\n" );
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document.write( "             |z+3| = |-4+3| = |-1| = 1,\r\n" );
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document.write( "             |z-2i| = |-4-2i| =  =  = ,\r\n" );
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document.write( "but  5 is not equal to  .\r\n" );
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\n" ); document.write( "\n" ); document.write( "So, it disproves the statement by @CPhill that z= 4 is a solution.\r
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\n" ); document.write( "\n" ); document.write( "It is not.\r
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