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Question

If |z|=1 and z1 z3z2 z3= ziz+i then z1, z2, z3 will be vertices of a
  1. None of these
  2. equilateral triangle
  3. acute angled triangle
  4. obtuse angled triangle


Solution

The correct option is A None of these
As |z|=1 lies on circle, so I and -I are extremities of this circle.
 
So, arg (ziz+i) = ±π2 ziz+i is purely imaginary
z1,z2,z3 represents vertices of right angled triangle

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