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AP EAMCET2016MathematicsComplex Number

If |z₁ |=1, |z₂ |=2, |z₃ |=3 and |9 z₁ z₂+4 z₁ z₃+z₂ z₃ |=12 , then the value of |z₁+z₂+z₃ | is

Options

  1. A3
  2. B4
  3. C8
  4. D2

Correct answer

D. 2

Step-by-step solution

We have, aligned & |z₁ |=1, |z₂ |=2, |z₃ |=3 and & |9 z₁ z₂+4 z₁ z₃+z₂ z₃ |=12 aligned Since, we know |z|^2=z z aligned & | array r z₃ z ₃ z₁ z₂+z₂ z ₂ z₁ z₂ +z₁ z ₁ z₂ z₃ array |=12 & |z₁ z₂ z₃ ( z ₃+ z ₂+ z ₁ ) |=12 & |z₁ z₂ z₃ | | z ₁+ z ₂+ z ₃ |=12 & |z₁ | |z₂ | |z₃ | | z ₁+ z ₂+ z ₂ |=12 & 1 2 3 | z ₁+ z ₂+ z ₃ |=12 & | z ₁+ z ₂+ z ₃ |=2 & |z₁+z₂+z₃ |=2 & aligned

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