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BITSAT2024MathematicsComplex NumberActual

If z₁, z₂, . . z_n are complex numbers such that |z₁ |= |z₂ |= . .= |z_n |=1 , then |z₁+z₂+ . .+z_n | is equal to

Options

  1. A|z₁ z₂ z₃ . . z_n |
  2. B|z₁ |+ |z₂ |+ . .+ |z_n |
  3. C| 1 z₁ + 1 z₂ + . .+ 1 z_n |
  4. Dn

Correct answer

C. | 1 z₁ + 1 z₂ + . .+ 1 z_n |

Step-by-step solution

|z₁ |= |z₂ |= |z₃ |= .= |z_n |=1 z₁ z ₁=z₂ z ₂=z₃ z ₃= =z_n z _n=1 z ₁= 1 z , z ₂= 1 z ₂ , z ₃= 1 z ₃ , , z _ n = 1 z _ n Now, |z₁+z₂+z₃+ .+z_n |= | z ₁+ z ₂+ + z _n | | z ₁+ z ₂+ z ₃+ .+ z _n |= | 1 z₁ + 1 z₂ + 1 z₃ + + 1 z_n |

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