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AP EAMCET202316 May 2023Evening ShiftMathematicsComplex NumberActual

If z ₁, z ₂, z ₃ are the vertices of an equilateral triangle and z is its circum centre, then

Options

  1. A|z-z₁ | |z-z₂ | = |z-z₃ | |z-z₁ |
  2. B|z-z₁ |+ |z-z₂ |+ |z-z₃ |=0
  3. C|z-z₁ | |z-z₂ | = |z-z₃ |
  4. D|z-z₁ |+ |z-z₂ | |z-z₃ | =1

Correct answer

A. |z-z₁ | |z-z₂ | = |z-z₃ | |z-z₁ |

Step-by-step solution

Given that z₁, z₂, z₃ are the vertices of an equilateral triangle and z is its circumcentre. aligned & |z-z₁ |= |z-z₂ |= |z-z₃ | & |z-z₁ | |z-z₂ | = |z-z₃ | |z-z₁ | aligned

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