document.write( "Question 1074905: Find all complex numbers $z$ such that $|z-1|=|z+3|=|z-i|$.\r
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Algebra.Com's Answer #689580 by ikleyn(52775)\"\" \"About 
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document.write( "The problem asks for a point z which in the complex plane is equidistant from complex points A = (1,0), B = (-3,0) and C = (0,i).\r\n" );
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document.write( "This point is actually the center of the circumscribed circle about these three points.\r\n" );
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document.write( "I can find this point without calculations (mentally).\r\n" );
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document.write( "The center of the circumscribed circle lies at the intersection of perpendicular bisectors to the sides. \r\n" );
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document.write( "The perpendicular bisector to the side AB is x = -1.\r\n" );
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document.write( "The perpendicular bisector to the side AC is the straight line y = x.\r\n" );
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document.write( "Their intersection is the point (-1,-1), which is the complex number -1-i.\r\n" );
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document.write( "Answer.  The complex number under the question is -1-i.\r\n" );
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