Question 1184217
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            This problem has a nice geometric interpretation.



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1 and -1 are selected points in the complex number plane.


For an arbitrary complex number z, the numbers z-1 and z+1 are vectors, connecting z with the points 1 and -1.



The condition that  {{{(z-1)/(z+1)}}}  is purely imaginary means that the vectors z-1 and z+1 are perpendicular.



So, the problem asks to find points z in complex plane, such that the "visibility angle" from z to 

these points "1" and "-1" is the right angle.


Or, in other terms, find points z in complex plane, such that the angle between the vectors z-1 and z+1 is the right angle.



Clearly, these points are on the unit circle, and they provide the right angle leaning on the segment [-1,1]

as on the diameter of the unit circle.   So, |z| = 1.    <U>ANSWER</U>
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