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Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

If z ₁, z ₂, z ₃ are the vertices of an equilateral triangle with centroid at origin & length of circum radius of triangle is 1 unit. Then which of the following may be the vertices of an equilateral triangle -

Options

  1. A- Z ₁,- Z ₂,- Z ₃
  2. B(z₁+ |z₂ | ), (z₂+ |z₃ | ), (z₃+ |z₁ | )
  3. C( z ₁+ z ₂ ) 2 , ( z ₂+ z ₃ ) 2 , ( z ₃+ z ₁ ) 2
  4. Dz₁ 2 |z₁ | , z₂ 2 |z₂ | , z₃ 2 |z₃ |

Correct answer

D. z₁ 2 |z₁ | , z₂ 2 |z₂ | , z₃ 2 |z₃ |

Step-by-step solution

For equilateral z ₁^2+ z ₂^2+ z ₃^2= z ₁ z ₂+ z ₂ z ₃+ z ₃ z ₁ (A) Which is satisfied by -z₁-z₂ & z₃ also similarly |z₁ |= |z₂ |= |z₃ |=1 (B) z ₁+1, z ₂+1, z ₃+1 are also satisfying the relation (C) are also vertices of equilateral . (D) z ₁ 2 , z ₂ 2 , z ₃ 2 are also vertices of an equilateral triangle.

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