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Question

The number of complex numbers z such that |z1|=|z+1|=|zi| equals
  1. 2
  2. 1
  3. 0


Solution

The correct option is C 1
Let z = x + iy
|z1|=|z+1|(x1)2+y2=(x+1)2+y2Re (z)=0x=0|z1|=|zi|(x1)2+y2=x2+(y1)2x=y|z+1|=|zi|(x+1)2+y2=x2+(y1)2
Only (0, 0) satisfies all conditions.

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